The classification of the finite simple groups

著者

• Gorenstein, Daniel
• Lyons, Richard
• Solomon, Ronald

書誌事項

The classification of the finite simple groups

Daniel Gorenstein, Richard Lyons, Ronald Solomon

（Mathematical surveys and monographs, v. 40）

American Mathematical Society, c1994-

• [no. 1]
• no. 2
• no. 3
• no. 4
• no. 5
• no. 6
• no. 7
• no. 8

注記

no. 2: pt. 1, chapter G, general group theory -- no. 3: pt. 1, chapter A, almost simple Κ-groups -- no. 4: pt. 2, chapters 1-4, uniqueness theorems -- no. 5: pt. 3, chapters 1-6, the generic case, stages 1-3a -- no. 6: pt. 4, the special odd case -- no. 7: pt. 3, chapters 7-11, the generic case, stages 3b and 4a -- no. 8: pt. 3, chapters 12-17, the genetic case, completed

Includes bibliographical references and indexes

内容説明・目次

内容説明

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.

目次

1: Part I. Chapter 1, Overview. 2: Introduction to the series. 3: The finite simple groups. 4: The structure of finite groups. 5: Classifying simple groups. 6: The background results. 7: Sketch of the simplified proof. 8: Additional comments. 9: Part I. Chapter 2, Outline of Proof. 10: Introduction. 11: The grids. 12: The uniqueness grid. 13: The classification grid: Generic and special simple groups. 14: The classification grid: The stages of the proof. 15: Principal techniques of the proof. 16: Notational conventions. 17: Background references. 18: Expository references. 19: Glossary. 20: Index. Part I. Chapter 1, Overview. Introduction to the series. The finite simple groups. The structure of finite groups. Classifying simple groups. The background results. Sketch of the simplified proof. Additional comments. Part I. Chapter 2, Outline of Proof. Introduction. The grids. The uniqueness grid. The classification grid: Generic and special simple groups. The classification grid: The stages of the proof. Principal techniques of the proof. Notational conventions. Background references. Expository references. Glossary. Index. Part I. Chapter 1, Overview. Introduction to the series. The finite simple groups. The structure of finite groups. Classifying simple groups. The background results. Sketch of the simplified proof. Additional comments. Part I. Chapter 2, Outline of Proof. Introduction. The grids. The uniqueness grid. The classification grid: Generic and special simple groups. The classification grid: The stages of the proof. Principal techniques of the proof. Notational conventions. Background references. Expository references. Glossary. Index

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詳細情報

• NII書誌ID(NCID): BA23942263
• ISBN:
  • 0821803344
  • 0821803905
  • 0821803913
  • 082181379X
  • 0821827766
  • 0821827774
  • 9780821840696
  • 9781470441890
• LCCN: 94023001
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Providence, R.I.
• ページ数/冊数: v.
• 大きさ: 26 cm
• 分類:
  • NDC9 : 411.63
  • NDC8 : 411.63
  • LCC : QA177
  • DC20 : 512/.2
• 件名:
  • LCSH : Finite simple groups
• 親書誌ID:
  • BA00134419