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Classification of the Finite Simple Groups, Number 9: Part V, Chapters 1-8: Theorem $C_5$ and Theorem $C_6$, Stage 1 [Minkštas viršelis]

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  • Formatas: Paperback / softback, 520 pages, aukštis x plotis: 254x178 mm, weight: 925 g
  • Serija: Mathematical Surveys and Monographs
  • Išleidimo metai: 30-Apr-2021
  • Leidėjas: American Mathematical Society
  • ISBN-10: 1470464373
  • ISBN-13: 9781470464370
Kitos knygos pagal šią temą:
Classification of the Finite Simple Groups, Number 9: Part V, Chapters 1-8: Theorem $C_5$ and Theorem $C_6$, Stage 1Didesnis paveikslėlis
  • Formatas: Paperback / softback, 520 pages, aukštis x plotis: 254x178 mm, weight: 925 g
  • Serija: Mathematical Surveys and Monographs
  • Išleidimo metai: 30-Apr-2021
  • Leidėjas: American Mathematical Society
  • ISBN-10: 1470464373
  • ISBN-13: 9781470464370
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9781470464370.html
Raktažodžiai:
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.
Preface xi
Chapter 1 Introduction to Theorem C5
1(10)
1 Statement of Theorem C5
1(2)
2 The Four Stages of the Proof of Theorem C5
3(8)
Chapter 2 General Group-Theoretic Lemmas, and Recognition Theorems
11(22)
1 Signalizer Functor Theory
11(2)
2 Signalizers
13(2)
3 Fusion
15(1)
4 p-Groups
16(3)
5 Uniqueness Subgroups
19(1)
6 Miscellaneous
20(3)
7 Components
23(1)
8 Rigidity, Semirigidity, and Terminality
24(3)
9 Centralizers of Components
27(2)
10 Recognition Theorems
29(4)
Chapter 3 Theorem 65: Stage 1
33(56)
1 Introduction
33(6)
2 The Strong Balance Lemma
39(1)
3 Theorem 1: Balance
39(5)
4 L2{pp) Field Triples
44(5)
5 Corollaries to Theorem 1
49(4)
6 Theorem 2: Signalizers in M
53(1)
7 The Centralizer of a Sylow 2-Subgroup of Op'(M)
54(5)
8 Sufficient Conditions for Faithful Action on T
59(1)
9 L2(pp) Field Triples Do Not Exist
60(2)
10 A Covering 2-Local Result
62(2)
11 Theorem 3: Γ°P,2(G) ≤ M
64(10)
12 Theorem 4: ΓP,2(G) ≤ M
74(7)
13 Theorem 5
81(8)
Chapter 4 Theorem 65: Stage 2
89(120)
1 Introduction
89(2)
2 The Principal Subsidiary Theorems
91(2)
3 Some Generalities
93(2)
4 Uniqueness Subgroups from p-Terminal p-Components
95(7)
5 Some Sporadic p-Components
102(1)
6 Theorem 1: Generalities
103(2)
7 Theorem 1: A-Terminal p-Components
105(10)
8 Theorem 1: The A-Terminality of A6
115(8)
9 Theorem 1: Standard 2-Components
123(20)
10 Theorem 2
143(1)
11 Corollaries: BtKp(G), and Components in p -- hev(p)
144(2)
12 Theorem 3: Regular Triples and Mates
146(12)
13 Theorem 3: p Must Be 3
158(2)
14 The Nondegenerate Case: Theorem 4
160(4)
15 Theorem 5: The Degenerate Case K > I
164(9)
16 Theorem 5: The Degenerate Case K = I
173(1)
17 Theorem 5: The Degenerate Case I < J
174(18)
18 Theorem 5: The Degenerate Case I = J
192(17)
Chapter 5 Theorem C5: Stage 3
209(28)
1 Introduction
209(1)
2 The Principal Subsidiary Theorems
210(1)
3 Theorem 1
211(8)
4 Maximal Symplectic Triples
219(5)
5 Theorem 2: p = 3 and Constrained Neighborhoods
224(2)
6 Theorem 2: Nonconstrained Neighborhoods of Type Fi'24
226(1)
7 Theorem 2: Nondegenerate Constrained Neighborhoods
227(4)
8 Theorem 2: Constrained Neighborhoods of Sporadic Type
231(6)
Chapter 6 Theorem C5: Stage 4
237(72)
1 Introduction
237(1)
2 The Case G* = Ω7(3) or Ω±8(3)
237(42)
3 The Case G* = Fi22
279(3)
4 The Case G* = Fi23
282(1)
5 The Case G* = Fi24 or Fi24
283(5)
6 The Case G* = F2
288(3)
7 The Case G* = Co1
291(1)
8 The Case G* = F1
291(1)
9 The Case G* = 2D5(2), 2E6(2), or U7(2)
292(17)
Chapter 7 Theorem C6: Stage 1
309(34)
1 Theorems C6 and C6
309(5)
2 The Proof of Theorem C7
314(1)
3 Theorems 1 and 1*
315(2)
4 Theorem 2
317(8)
5 Theorem 2 Completed: The U3(8) Case
325(18)
Chapter 8 Preliminary Properties of 3C-Groups
343(172)
1 Small Groups
343(2)
2 Outer Automorphisms and Covering Groups
345(2)
3 Pumpups and Subcomponents
347(33)
3.1 Key Generalities
347(2)
3.2 Pumpups of Specific Groups
349(4)
3.3 Pumpups and p-Rank
353(3)
3.4 Pumpups and Schur Multipliers
356(1)
3.5 Pumpups of Ae
357(2)
3.6 p-Subcomponents and q-Subcomponents, p ≠ q
359(2)
3.7 Action of CAut(K)(x) on E(CK(x))
361(7)
3.8 Pumpups and the Sets 6P, p Prime
368(10)
3.9 Solvable Components
378(1)
3.10 Other
379(1)
4 Computations in Groups of Lie Type
380(4)
5 Representations
384(9)
6 Factorizations
393(1)
7 Signalizers and Balance
394(5)
7.1 Signalizers
394(3)
7.2 Balance and Cores
397(2)
8 Generation
399(25)
8.1 Generation with respect to Non-elementary p-Groups, p = 2
399(1)
8.2 Generation with respect to Elementary Abelian p-Groups, p = 2
400(3)
8.3 Generation with respect to Elementary Abelian p-Groups, p > 2
403(12)
8.4 Generation with respect to Non-elementary p-Groups, p > 2
415(7)
8.5 Other
422(2)
9 p-Structure, p odd
424(11)
9.1 Self-centralizing Ep2-Subgroups, p ≥ 5
424(2)
9.2 Sylow p-Subgroups P, and Z(P) and J(P)
426(4)
9.3 Other p-Subgroups
430(4)
9.4 Other
434(1)
10 2-Structure
435(28)
10.1 Orthogonal Groups over F3
435(11)
10.2 Sylow 2-Subgroups and Their Overgroups in Quasisimple K-Groups
446(10)
10.3 Other Involution Centralizers
456(5)
10.4 Other
461(2)
11 C2-Groups and Cp-Groups, p odd
463(6)
12 {2,p}-Structure
469(23)
12.1 Wide 2-Components
469(3)
12.2 Subgroups of Order 2p
472(5)
12.3 Components for Permutable Subgroups of Orders 2 and p
477(5)
12.4 2-Local p-Rank
482(2)
12.5 Mates
484(1)
12.6 P-Components in C2-Groups
485(5)
12.7 Other
490(2)
13 {2,3}-Neighborhoods
492(3)
14 Semirigidity
495(2)
14.1 Conditions for Semirigidity
495(2)
14.2 Z4-Semirigidity
497(1)
15 Miscellaneous
497(8)
16 Preliminary Lemmas for Theorem C6: Stage 1
505(10)
16.1 p-Ranks, Cip-Groups, and Flat Cp-Groups
505(1)
16.2 Pumpups and Subcomponents
506(4)
16.3 3-Structure
510(2)
16.4 Other
512(3)
Bibliography 515(4)
Index 519
Inna Capdeboscq, University of Warwick, Coventry, United Kingdom.

Daniel Gorenstein, Rutgers University, Piscataway, NJ.

Richard Lyons, Rutgers University, Piscataway, NJ.

Ronald Solomon, The Ohio State University, Columbus, OH.