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nexusstc/The Classification of the Finite Simple Groups, Number 8/359c4179b6b2e5d8b56ee681fee122ee.pdf

The Classification of the Finite Simple Groups, Number 8 Daniel Gorenstein, Richard Lyons, Ronald Solomon American Mathematical Society, Mathematical Surveys and Monographs 040-8, 2018

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[2] [1994] [Gorenstein, D., Lyons, R. and Solomon, R.] The Classification of the Finite Simple Groups, Number 2, Part I, Chapter G: General Group Theory Daniel Gorenstein, Richard Lyons, Ronald Solomon. No.2, Part I, Chapter G: General group theory American Mathematical Society, Mathematical surveys and monographs 40, 1-<6 >, Number 2, 1996

The classification of the finite simple groups is one of the major feats of contemporary mathematical research, but its proof has never been completely extricated from the journal literature in which it first appeared. This book serves as an introduction to a series devoted to organizing and simplifying the proof. The purpose of the series is to present as direct and coherent a proof as is possible with existing techniques. This first volume, which sets up the structure for the entire series, begins with largely informal discussions of the relationship between the Classification Theorem and the general structure of finite groups, as well as the general strategy to be followed in the series and a comparison with the original proof. Also listed are background results from the literature that will be used in subsequent volumes. Next, the authors formally present the structure of the proof and the plan for the series of volumes in the form of two grids, giving the main case division of the proof as well as the principal milestones in the analysis of each case. Thumbnail sketches are given of the ten or so principal methods underlying the proof. This book is intended for first- or second-year graduate students/researchers in group theory.

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lgli/K:\_add\!woodhead\!\kolxoz\Gorenstein D., Lyons R., Solomon R. The classification of the finite simple groups. Number 4. Part II. Chapters 1--4 (SURV040-4, AMS, 1999)(ISBN 9780821813799)(600dpi)(T)(O)(361s)_MAtg_.djvu

[1999] [Gorenstein, D., Lyons, R. and Solomon, R.] The Classification of the Finite Simple Groups, Number 4. Part II, Chapters 1-4: Uniqueness Theorems Lyons, Richard; Gorenstein, Daniel; Solomon, Ronald American Mathematical Society, Mathematical surveys and monographs Volume 40 Number 4, 1999

After three introductory volumes on the classification of the finite simple groups, (Mathematical Surveys and Monographs, Volumes 40.1, 40.2, and 40.3), the authors now start the proof of the classification theorem: They begin the analysis of a minimal counterexample $G$ to the theorem. Two fundamental and powerful theorems in finite group theory are examined: the Bender-Suzuki theorem on strongly embedded subgroups (for which the non-character-theoretic part of the proof is provided) and Aschbacher's Component theorem. Included are new generalizations of Aschbacher's theorem which treat components of centralizers of involutions and $p$-components of centralizers of elements of order $p$ for arbitrary primes $p$. This book, with background from sections of the previous volumes, presents in an approachable manner critical aspects of the classification of finite simple groups. Features: Treatment of two fundamental and powerful theorems in finite group theory. Proofs that are accessible and largely self-contained. New results generalizing Aschbacher's Component theorem and related component uniqueness theorems.

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nexusstc/The Classification of the Finite Simple Groups, 4, Part II, Chapters 1-4: Uniqueness Theorems/1ea96f74e3b0f5a4a48511ae43d6b76a.pdf

The Classification of the Finite Simple Groups, 4, Part II, Chapters 1-4: Uniqueness Theorems 4 Daniel Gorenstein, Richard Lyons, Ronald Solomon American Mathematical Society, Mathematical Surveys and Monographs, 40, No 4, 40, No 4, 1994

The classification of the finite simple groups is one of the major feats of contemporary mathematical research, but its proof has never been completely extricated from the journal literature in which it first appeared. This book serves as an introduction to a series devoted to organizing and simplifying the proof. The purpose of the series is to present as direct and coherent a proof as is possible with existing techniques. This first volume, which sets up the structure for the entire series, begins with largely informal discussions of the relationship between the Classification Theorem and the general structure of finite groups, as well as the general strategy to be followed in the series and a comparison with the original proof. Also listed are background results from the literature that will be used in subsequent volumes. Next, the authors formally present the structure of the proof and the plan for the series of volumes in the form of two grids, giving the main case division of the proof as well as the principal milestones in the analysis of each case. Thumbnail sketches are given of the ten or so principal methods underlying the proof. This book is intended for first- or second-year graduate students/researchers in group theory.

English [en] · PDF · 42.7MB · 1994 · 📘 Book (non-fiction) · 🚀/lgli/lgrs/nexusstc/zlib · Save

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lgli/K:\_add\!woodhead\!\kolxoz\Gorenstein D., Lyons R., Solomon R. The classification of the finite simple groups. Number 5. Part III. Chapters 1--6 (SURV040-5, AMS, 2002)(ISBN 9780821827765)(600dpi)(T)(O)(482s)_MAtg_.djvu

[2002] [Gorenstein, D., Lyons, R. and Solomon, R.] The Classification of the Finite Simple Groups, Number 5. Part III, Chapters 1-6: The Generic Case, Stages 1-3a Lyons, Richard; Gorenstein, Daniel; Solomon, Ronald American Mathematical Society, Mathematical surveys and monographs, Volume 40, Number 5, 2002

The classification of finite simple groups is a landmark result of modern mathematics. The original proof is spread over scores of articles by dozens of researchers. In this multivolume book, the authors are assembling the proof with explanations and references. It is a monumental task. The book, along with background from sections of the previous volumes, presents critical aspects of the classification. In four prior volumes (Surveys of Mathematical Monographs, Volumes 40.1, 40.2, 40.3, and 40.4), the authors began the proof of the classification theorem by establishing certain uniqueness and preuniqueness results. In this volume, they now begin the proof of a major theorem from the classification grid, namely Theorem $\mathcal{C}\_7$. The book is suitable for graduate students and researchers interested in group theory

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The Classification of the Finite Simple Groups, Number 8: Part III, Chapters 12–17: The Generic Case, Completed Gorenstein, Daniel; Solomon, Ronald; Lyons, Richard; American Mathematical Society Providence, R.I.: American Mathematical Society, American Mathematical Society, Providence, Rhode Island, 2018

The classification of finite simple groups is a landmark result of modern mathematics. The multipart series of monographs which is being published by the AMS (Volume 40.1–40.7 and future volumes) represents the culmination of a century-long project involving the efforts of scores of mathematicians published in hundreds of journal articles, books, and doctoral theses, totaling an estimated 15,000 pages. This part 7 of the series is the middle of a trilogy (Volume 40.5, Volume 40.7, and forthcoming Volume 40.8) treating the Generic Case, i.e., the identification of the alternating groups of degree at least 13 and most of the finite simple groups of Lie type and Lie rank at least 4. Moreover, Volumes 40.4–40.8 of this series will provide a complete treatment of the simple groups of odd type, i.e., the alternating groups (with two exceptions) and the groups of Lie type defined over a finite field of odd order, as well as some of the sporadic simple groups. In particular, this volume completes the construction, begun in Volume 40.5, of a collection of neighboring centralizers of a particularly nice form. All of this is then applied to complete the identification of the alternating groups of degree at least 13. The book is suitable for graduate students and researchers interested in the theory of finite groups.

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nexusstc/The Classification of the Finite Simple Groups, Number 9/539959f38604462b3adb3ca9dee6c0b8.pdf

The Classification of the Finite Simple Groups, Number 9, Part 9: Part V, Chapters 1-8: Theorem C5 and Theorem C6, Stage 1 Inna Capdeboscq; Daniel Gorenstein; Richard Lyons; Ronald Solomon, American Mathematical Society, Mathematical surveys and monographs, 40,9, Providence American Mathematical Society, 2021

This book is the ninth volume in a series whose goal is to furnish a careful and largely self-contained proof of the classification theorem for the finite simple groups. Having completed the classification of the simple groups of odd type as well as the classification of the simple groups of generic even type (modulo uniqueness theorems to appear later), the current volume begins the classification of the finite simple groups of special even type. The principal result of this volume is a classification of the groups of bicharacteristic type, i.e., of both even type and of $p$-type for a suitable odd prime $p$. It is here that the largest sporadic groups emerge, namely the Monster, the Baby Monster, the largest Conway group, and the three Fischer groups, along with six finite groups of Lie type over small fields, several of which play a major role as subgroups or sections of these sporadic groups.

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lgli/M_Mathematics/MA_Algebra/MAtg_Group theory/Gorenstein D., Lyons R., Solomon R. Classification of finite simple groups 1 (AMS survey 40 no.1, 1994, 2000)(T)(ISBN 0821803344)(176s).djvu

Classification of finite simple groups 1 Number 1 Daniel Gorenstein, Richard Lyons, Ronald Solomon American Mathematical Society, AMS survey 40, Number 1, 1994

The classification of the finite simple groups is one of the major feats of contemporary mathematical research, but its proof has never been completely extricated from the journal literature in which it first appeared. This book serves as an introduction to a series devoted to organizing and simplifying the proof. The purpose of the series is to present as direct and coherent a proof as is possible with existing techniques. This first volume, which sets up the structure for the entire series, begins with largely informal discussions of the relationship between the Classification Theorem and the general structure of finite groups, as well as the general strategy to be followed in the series and a comparison with the original proof. Also listed are background results from the literature that will be used in subsequent volumes. Next, the authors formally present the structure of the proof and the plan for the series of volumes in the form of two grids, giving the main case division of the proof as well as the principal milestones in the analysis of each case. Thumbnail sketches are given of the ten or so principal methods underlying the proof. This book is intended for first- or second-year graduate students/researchers in group theory.

English [en] · DJVU · 1.3MB · 1994 · 📘 Book (non-fiction) · 🚀/lgli/lgrs/nexusstc/zlib · Save

lgli/M_Mathematics/MA_Algebra/MAtg_Group theory/Gorenstein D., Lyons R., Solomon R. Classification of finite simple groups 1 (AMS survey 40 no.1, 1994, 2000)(176s).pdf

Classification of finite simple groups 1 Number 1 Daniel Gorenstein, Richard Lyons, Ronald Solomon American Mathematical Society, AMS survey 40, Number 1, 1994

The classification of the finite simple groups is one of the major feats of contemporary mathematical research, but its proof has never been completely extricated from the journal literature in which it first appeared. This book serves as an introduction to a series devoted to organizing and simplifying the proof. The purpose of the series is to present as direct and coherent a proof as is possible with existing techniques. This first volume, which sets up the structure for the entire series, begins with largely informal discussions of the relationship between the Classification Theorem and the general structure of finite groups, as well as the general strategy to be followed in the series and a comparison with the original proof. Also listed are background results from the literature that will be used in subsequent volumes. Next, the authors formally present the structure of the proof and the plan for the series of volumes in the form of two grids, giving the main case division of the proof as well as the principal milestones in the analysis of each case. Thumbnail sketches are given of the ten or so principal methods underlying the proof. This book is intended for first- or second-year graduate students/researchers in group theory.

English [en] · PDF · 1.3MB · 1994 · 📘 Book (non-fiction) · 🚀/lgli/lgrs/nexusstc/zlib · Save

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nexusstc/The Classification of the Finite Simple Groups/f7ee56fb1bf35466a38c18e6fe8c340a.pdf

[1998] [Gorenstein, D., Lyons, R. and Solomon, R.] The Classification of the Finite Simple Groups, Number 3. Part I, Chapter A: Almost Simple K-Groups Daniel Gorenstein, Richard Lyons, Ronald Solomon American Mathematical Society, Mathematical Surveys and Monographs, 40, No 1, 40, No 1, 1994

The classification of the finite simple groups is one of the major feats of contemporary mathematical research, but its proof has never been completely extricated from the journal literature in which it first appeared. This book serves as an introduction to a series devoted to organizing and simplifying the proof. The purpose of the series is to present as direct and coherent a proof as is possible with existing techniques. This first volume, which sets up the structure for the entire series, begins with largely informal discussions of the relationship between the Classification Theorem and the general structure of finite groups, as well as the general strategy to be followed in the series and a comparison with the original proof. Also listed are background results from the literature that will be used in subsequent volumes. Next, the authors formally present the structure of the proof and the plan for the series of volumes in the form of two grids, giving the main case division of the proof as well as the principal milestones in the analysis of each case. Thumbnail sketches are given of the ten or so principal methods underlying the proof. This book is intended for first- or second-year graduate students/researchers in group theory.

English [en] · PDF · 50.6MB · 1994 · 📘 Book (non-fiction) · 🚀/lgli/lgrs/nexusstc/zlib · Save

nexusstc/The Classification of the Finite Simple Groups 3. Part I, Chapter A: Almost Simple K-Groups/0f47d9db1dcaf643d21fa0d0e80e2c40.djvu

The Classification of the Finite Simple Groups 3. Part I, Chapter A: Almost Simple K-Groups Gorenstein D., Lyons R., Solomon R. American Mathematical Society, Mathematical Surveys and Monographs 40.3, 1998

This book offers a single source of basic facts about the structure of the finite simple groups with emphasis on a detailed description of their local subgroup structures, coverings and automorphisms. The method is by examination of the specific groups, rather than by the development of an abstract theory of simple groups. While the purpose of the book is to provide the background for the proof of the classification of the finite simple groups—dictating the choice of topics—the subject matter is covered in such depth and detail that the book should be of interest to anyone seeking information about the structure of the finite simple groups. This volume offers a wealth of basic facts and computations. Much of the material is not readily available from any other source. In particular, the book contains the statements and proofs of the fundamental Borel-Tits Theorem and Curtis-Tits Theorem. It also contains complete information about the centralizers of semisimple involutions in groups of Lie type, as well as many other local subgroups.

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nexusstc/The Classification of the Finite Simple Groups, Number 5; Part III, Chapters 1-6: The Generic Case, Stages l-3a/2a0c321ff71481d4b61bb675ef3f8a8e.pdf

The Classification of the Finite Simple Groups, Number 5; Part III, Chapters 1-6: The Generic Case, Stages l-3a Daniel Gorenstein, Richard Lyons, Ronald Solomon American Mathematical Society, Mathematical Surveys and Monographs, 40, No. 5, 2002

The classification of finite simple groups is a landmark result of modern mathematics. The original proof is spread over scores of articles by dozens of researchers. In this multivolume book, the authors are assembling the proof with explanations and references. It is a monumental task. The book, along with background from sections of the previous volumes, presents critical aspects of the classification. In four prior volumes (Surveys of Mathematical Monographs, Volumes 40.1, 40.2, 40.3, and 40.4), the authors began the proof of the classification theorem by establishing certain uniqueness and preuniqueness results. In this volume, they now begin the proof of a major theorem from the classification grid, namely Theorem $\mathcal{C}\_7$. The book is suitable for graduate students and researchers interested in group theory.

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lgli/M_Mathematics/MA_Algebra/MAtg_Group theory/Gorenstein D., Lyons R., Solomon R. Classification of finite simple groups 2. Part I, chapter G.. general group theory (AMS survey 40 no.2, 1996)(ISBN 0821803905)(T)(232s)_MAtg_.djvu

Classification of finite simple groups 2. Part I, chapter G: general group theory Number 2 Daniel Gorenstein, Richard Lyons, Ronald Solomon. No.2, Part I, Chapter G: General group theory American Mathematical Society, AMS survey 40, Number 2, 1995

The Classification Theorem is one of the main achievements of 20th century mathematics, but its proof has not yet been completely extricated from the journal literature in which it first appeared. This is the second volume in a series devoted to the presentation of a reorganized and simplified proof of the classification of the finite simple groups. The authors present (with either proof or reference to a proof) those theorems of abstract finite group theory, which are fundamental to the analysis in later volumes in the series. This volume provides a relatively concise and readable access to the key ideas and theorems underlying the study of finite simple groups and their important subgroups. The sections on semisimple subgroups and subgroups of parabolic type give detailed treatments of these important subgroups, including some results not available until now or available only in journal literature. The signalizer section provides an extensive development of both the Bender Method and the Signalizer Functor Method, which play a central role in the proof of the Classification Theorem. This book would be a valuable companion text for a graduate group theory course.

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lgli/Capdeboscq I., Gorenstein D., Lyons R., Solomon R. The classification of the finite simple groups. Number 10 (surv-40.10, AMS, 2023)(ISBN 9781470475536)(O)(587s)_MAtg_.pdf

The Classification of the Finite Simple Groups, Number 10 Inna Capdeboscq, Daniel Gorenstein, Richard Lyons, Ronald Solomon American Mathematical Society, 2023

This book is the tenth in a series of volumes whose aim is to provide a complete proof of the classification theorem for the finite simple groups based on a fairly short and clearly enumerated set of background results. Specifically, this book completes our identification of the simple groups of bicharacteristic type begun in the ninth volume of the series (see SURV/40.9). This is a fascinating set of simple groups which have properties in common with matrix groups (or, more generally, groups of Lie type) defined both over fields of characteristic 2 and over fields of characteristic 3. This set includes 11 of the celebrated 26 sporadic simple groups along with several of their large simple subgroups. Together with SURV/40.9, this volume provides the first unified treatment of this class of simple groups.

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lgli/75/M_Mathematics/MA_Algebra/MAtg_Group theory/Gorenstein D., Lyons R., Solomon R. The classification of the finite simple groups. Number 2. Part I. Chapter G (SURV040-2, AMS, 1996)(ISBN 9780821803905)(600dpi)(T)(O)(234s)_MAtg_.djvu

The classification of the finite simple groups. Number 2. Part I. Chapter G Daniel Gorenstein, Richard Lyons, Ronald Solomon. No.2, Part I, Chapter G: General group theory American Mathematical Society, Mathematical Surveys and Monographs 040-2, 1996

The Classification Theorem is one of the main achievements of 20th century mathematics, but its proof has not yet been completely extricated from the journal literature in which it first appeared. This is the second volume in a series devoted to the presentation of a reorganized and simplified proof of the classification of the finite simple groups. The authors present (with either proof or reference to a proof) those theorems of abstract finite group theory, which are fundamental to the analysis in later volumes in the series. This volume provides a relatively concise and readable access to the key ideas and theorems underlying the study of finite simple groups and their important subgroups. The sections on semisimple subgroups and subgroups of parabolic type give detailed treatments of these important subgroups, including some results not available until now or available only in journal literature. The signalizer section provides an extensive development of both the Bender Method and the Signalizer Functor Method, which play a central role in the proof of the Classification Theorem. This book would be a valuable companion text for a graduate group theory course.

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nexusstc/The Classification of the Finite Simple Groups, Number 7/3544800aa0e2f4c94bbaf11ce7914101.pdf

The Classification of the Finite Simple Groups, Number 7: Part III, Chapters 7–11: The Generic Case, Stages 3b and 4a Daniel Gorenstein; Richard Lyons; Ronald Solomon American Mathematical Society, Mathematical Surveys and Monographs, MATHEMATICAL Surveys and Monographs 40.7, 2018

The classification of finite simple groups is a landmark result of modern mathematics. The multipart series of monographs which is being published by the AMS (Volume 40.1–40.7 and future volumes) represents the culmination of a century-long project involving the efforts of scores of mathematicians published in hundreds of journal articles, books, and doctoral theses, totaling an estimated 15,000 pages. This part 7 of the series is the middle of a trilogy (Volume 40.5, Volume 40.7, and forthcoming Volume 40.8) treating the Generic Case, i.e., the identification of the alternating groups of degree at least 13 and most of the finite simple groups of Lie type and Lie rank at least 4. Moreover, Volumes 40.4–40.8 of this series will provide a complete treatment of the simple groups of odd type, i.e., the alternating groups (with two exceptions) and the groups of Lie type defined over a finite field of odd order, as well as some of the sporadic simple groups. In particular, this volume completes the construction, begun in Volume 40.5, of a collection of neighboring centralizers of a particularly nice form. All of this is then applied to complete the identification of the alternating groups of degree at least 13. The book is suitable for graduate students and researchers interested in the theory of finite groups.

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lgli/75/M_Mathematics/MA_Algebra/MAtg_Group theory/Gorenstein D., Lyons R., Solomon R. The classification of the finite simple groups. Number 6. Part IV (SURV040-6, AMS, 2005)(ISBN 9780821827772)(600dpi)(T)(O)(545s)_MAtg_.djvu

The classification of the finite simple groups. Number 6. Part IV Daniel Gorenstein, Richard Lyons, Ronald Solomon. Pt. 4, The special odd case American Mathematical Society, Mathematical Surveys and Monographs 040-6, 2005

The classification of finite simple groups is a landmark result of modern mathematics. The original proof is spread over scores of articles by dozens of researchers. In this multivolume book, the authors are assembling the proof with explanations and references. It is a monumental task. The book, along with background from sections of the previous volumes, presents critical aspects of the classification. Continuing the proof of the classification theorem which began in the previous five volumes (Surveys of Mathematical Monographs, Volumes 40.1.E, 40.2, 40.3, 40.4, and 40.5), in this volume, the authors provide the classification of finite simple groups of special odd type (Theorems $\mathcal{C}\_2$ and $\mathcal{C}\_3$, as stated in the first volume of the series). The book is suitable for graduate students and researchers interested in group theory

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nexusstc/The Classification of the Finite Simple Groups, Number 10/c1f7d4d764a26ece6051367ce948ab1c.pdf

The Classification of the Finite Simple Groups, Number 10 10 Inna Capdeboscq, Daniel Gorenstein, Richard Lyons, Ronald Solomon American Mathematical Society, Mathematical Surveys and Monographs, Mathematical Surveys and Monographs 40.10, 10, 2023

This book is the tenth in a series of volumes whose aim is to provide a complete proof of the classification theorem for the finite simple groups based on a fairly short and clearly enumerated set of background results. Specifically, this book completes our identification of the simple groups of bicharacteristic type begun in the ninth volume of the series (see SURV/40.9). This is a fascinating set of simple groups which have properties in common with matrix groups (or, more generally, groups of Lie type) defined both over fields of characteristic 2 and over fields of characteristic 3. This set includes 11 of the celebrated 26 sporadic simple groups along with several of their large simple subgroups. Together with SURV/40.9, this volume provides the first unified treatment of this class of simple groups.

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nexusstc/The Classification of the Finite Simple Groups, Number 6, Part IV: The Special Odd Case/b3a1499bc25747e27f2948eee5bd812d.pdf

The Classification of the Finite Simple Groups, Number 6, Part IV: The Special Odd Case 6 Daniel Gorenstein, Richard Lyons, Ronald Solomon. Pt. 4, The special odd case American Mathematical Society, Mathematical Surveys and Monographs, 40, Number 6, 2004

The classification of finite simple groups is a landmark result of modern mathematics. The original proof is spread over scores of articles by dozens of researchers. In this multivolume book, the authors are assembling the proof with explanations and references. It is a monumental task. The book, along with background from sections of the previous volumes, presents critical aspects of the classification. Continuing the proof of the classification theorem which began in the previous five volumes (Surveys of Mathematical Monographs, Volumes 40.1.E, 40.2, 40.3, 40.4, and 40.5), in this volume, the authors provide the classification of finite simple groups of special odd type (Theorems $\mathcal{C}\_2$ and $\mathcal{C}\_3$, as stated in the first volume of the series). The book is suitable for graduate students and researchers interested in group theory.

English [en] · PDF · 60.7MB · 2004 · 📘 Book (non-fiction) · 🚀/lgli/lgrs/nexusstc/zlib · Save

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lgli/75/M_Mathematics/MA_Algebra/MAtg_Group theory/Gorenstein D., Lyons R., Solomon R. The classification of the finite simple groups. Number 3. Part I. Chapter A (SURV040-3, AMS, 1998)(ISBN 9780821803912)(600dpi)(T)(O)(439s)_MAtg_.djvu

The classification of the finite simple groups, number 3. Part I. Chapter A Daniel Gorenstein, Richard Lyons, Ronald Solomon. No.2, Part I, Chapter G: General group theory American Mathematical Society, Mathematical Surveys and Monographs 040.3, 1, 1998

This book offers a single source of basic facts about the structure of the finite simple groups with emphasis on a detailed description of their local subgroup structures, coverings and automorphisms. The method is by examination of the specific groups, rather than by the development of an abstract theory of simple groups. While the purpose of the book is to provide the background for the proof of the classification of the finite simple groups--dictating the choice of topics--the subject matter is covered in such depth and detail that the book should be of interest to anyone seeking information about the structure of the finite simple groups. This volume offers a wealth of basic facts and computations. Much of the material is not readily available from any other source. In particular, the book contains the statements and proofs of the fundamental Borel-Tits Theorem and Curtis-Tits Theorem. It also contains complete information about the centralizers of semisimple involutions in groups of Lie type, as well as many other local subgroups

English [en] · DJVU · 4.4MB · 1998 · 📘 Book (non-fiction) · 🚀/lgli/lgrs/nexusstc/zlib · Save

upload/newsarch_ebooks_2025_10/2017/02/13/0821809601_book.djvu

The Classification of the Finite Simple Groups (Mathematical Surveys and Monographs, 40, No 1) Daniel Gorenstein; Richard Lyons; Ronald M. Solomon American Mathematical Society, Mathematical Surveys and Monographs, Mathematical Surveys and Monographs, 40, No 1, 1994

The classification of the finite simple groups is one of the major feats of contemporary mathematical research, but its proof has never been completely extricated from the journal literature in which it first appeared. This book serves as an introduction to a series devoted to organizing and simplifying the proof. The purpose of the series is to present as direct and coherent a proof as is possible with existing techniques. This first volume, which sets up the structure for the entire series, begins with largely informal discussions of the relationship between the Classification Theorem and the general structure of finite groups, as well as the general strategy to be followed in the series and a comparison with the original proof. Also listed are background results from the literature that will be used in subsequent volumes. Next, the authors formally present the structure of the proof and the plan for the series of volumes in the form of two grids, giving the main case division of the proof as well as the principal milestones in the analysis of each case. Thumbnail sketches are given of the ten or so principal methods underlying the proof. This book is intended for first- or second-year graduate students/researchers in group theory.

English [en] · DJVU · 1.5MB · 1994 · 📘 Book (non-fiction) · 🚀/lgli/lgrs/nexusstc/upload/zlib · Save

nexusstc/The Classification of the Finite Simple Groups/c19674ac6ec262df35abca7adfa52f95.pdf

The Classification of the Finite Simple Groups (Mathematical Surveys and Monographs, 40, No 1) Daniel Gorenstein; Richard Lyons; Ronald M. Solomon American Mathematical Society, Mathematical Surveys and Monographs, Mathematical Surveys and Monographs, 40, No 1, 1994

The classification of the finite simple groups is one of the major feats of contemporary mathematical research, but its proof has never been completely extricated from the journal literature in which it first appeared. This book serves as an introduction to a series devoted to organizing and simplifying the proof. The purpose of the series is to present as direct and coherent a proof as is possible with existing techniques. This first volume, which sets up the structure for the entire series, begins with largely informal discussions of the relationship between the Classification Theorem and the general structure of finite groups, as well as the general strategy to be followed in the series and a comparison with the original proof. Also listed are background results from the literature that will be used in subsequent volumes. Next, the authors formally present the structure of the proof and the plan for the series of volumes in the form of two grids, giving the main case division of the proof as well as the principal milestones in the analysis of each case. Thumbnail sketches are given of the ten or so principal methods underlying the proof. This book is intended for first- or second-year graduate students/researchers in group theory.

English [en] · PDF · 21.5MB · 1994 · 📘 Book (non-fiction) · 🚀/lgli/lgrs/nexusstc/zlib · Save