The classification of the finite simple groups. Number 5 : Part III, chapters 1-6 : the generic case, stages 1-3a / Daniel Gorenstein, Richard Lyons, Ronald Solomon.

Format:

Book

Author/Creator:

Gorenstein, Daniel, author.

Lyons, Richard, author.

Solomon, Ronald, author.

Series:

Mathematical surveys and monographs ; volume 40, number 5.

Mathematical surveys and monographs ; volume 40, number 5

Language:

English

Subjects (All):

Finite simple groups.

Physical Description:

1 online resource (482 p.)

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2002]

Language Note:

English

Summary:

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 graduatestudents and researchers interested in group theory.

Contents:

""Contents""; ""Preface""; ""Part III, Chapters 1�6: The Generic Case, Stages 1�3a""; ""Chapter 1. Theorem C[sub(7)]: General Introduction""; ""1. Generic Simple Groups""; ""2. The Special Type Hypothesis""; ""3. Statement of Theorem C*[sub(7)]""; ""4. Comments on the Proof of Theorem C*[sub(7)]""; ""Chapter 2. General Group-Theoretic Results""; ""1. p-Components, Pumpups and p-Terminally""; ""2. Stability and the B[sub(p)]-Property""; ""3. Balance and Signalizers""; ""4. 2-Terminal Intrinsic 2-Components""; ""5. Coverings""; ""6. Fusion""; ""7. p-Groups""; ""8. Quasi- p-Cycles""

""9. Miscellaneous""""Chapter 3. Theorem C*[sub(7)]: Stage 1""; ""1. Introduction""; ""2. p-Sources""; ""3. Failure of Local Balance""; ""4. The Subsidiary Theorems, General Case""; ""5. The Preferred Set J[sup(o)][sub(p)](G)""; ""6. The Remaining Subsidiary Theorems""; ""7. Theorem 1: The 2A[sub(n)] Case""; ""8. The Tight Sp[sub(4)](q) Case""; ""9. Theorem 2: The Nonsolvable Case""; ""10. Theorem 2: The Solvable p-Component Case""; ""11. Corollary 2 and Extended p-Sources""; ""12. Theorem 3: The Wide Lie Type Case, p = 2""

""13. Theorem 3: The A[sub(n)] Case, n > 12, and the F[sub(5)] Case, p = 2""""14. The Extended (x, K) p-Source Strategy""; ""15. Bootstrapping from an Easier Level of Balance""; ""16. The L[sub(3)](4) Case of the Reduction""; ""17. Applications to Extended p-Sources""; ""18. Theorem 4: The A[sub(n)] Case""; ""19. Theorem 4: The Wide Lie Type Case""; ""20. Completion of the Proof for p > 2: Theorem 5""; ""21. Theorem 6: The Sporadic Cases""; ""22. The A[sub(n)] Case, n = 9, 10, or 11""; ""23. Theorem 7, Case 1""; ""24. Theorem 9""; ""25. Theorem 7, Case 2: 5/2-Balance""

""26. Theorem 7, Case 2: Θ'[sub(5/2)](GB) Is Nontrivial""; ""27. Theorem 7, Case 2: Bootstrapping""; ""28. Theorem 7: Case 3""; ""29. Theorem 8: The Extended 2-Source Case""; ""30. Fusion and Pumpups""; ""31. Failure of 3/2-Balance""; ""Chapter 4. Theorem C*[sub(7)]: Stage 2""; ""1. Introduction""; ""2. The Subsidiary Theorems""; ""3. Properties of k-Groups and p-Sources""; ""4. Proposition 1""; ""5. Theorem 1: K Lies in M""; ""6. The Embedding of K in M: The Diagonal Case, p > 2""; ""7. The Embedding of K in M: The General Case""; ""8. Theorem 2""; ""9. Corollary 2""

""10. Controlling Layers of Centralizers of Elements of Order p""""11. Theorem 3: p-Component Preuniqueness Subgroups""; ""12. H = K: The Non-Strongly-Closed (S)L[sup(+)][sub(p)](q) Case""; ""13. H = K: The Non-Strongly-Closed Case""; ""14. H = K: The Strongly Closed Case""; ""15. The Embedding of Γ[sub(A,1)](G)""; ""16. Connecting""; ""17. Theorem 4""; ""18. Theorem 5""; ""19. Appendix I: The Semisimple- Neighbor Strongly-Closed Case""; ""20. Appendix II: p-Terminal Pairs with Wide Centralizers""; ""Chapter 5. Theorem C*[sub(7)]: Stage 3a""; ""1. Introduction""

""2. The Subsidiary Theorems""

Notes:

Description based upon print version of record.

Includes bibliographical references.

Description based on online resource; title from PDF title page (ebrary, viewed May 23, 2014).

ISBN:

1-4704-1270-5