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Preface | p. ix |
The Special Odd Case | |
General Introduction to the Special Odd Case | p. 1 |
The Goals: Theorems [characters not reproducible] and [characters not reproducible] | p. 1 |
Theorems [characters not reproducible] and [characters not reproducible] | p. 2 |
General Comments on the Proof of Theorem [characters not reproducible] | p. 6 |
Theorem [characters not reproducible] and Its Proof | p. 9 |
General Lemmas | p. 13 |
The Bender/Glauberman Method | p. 13 |
p-Groups and Coprime Action | p. 18 |
Transfer and Fusion | p. 28 |
2-Components and 2-Groups | p. 32 |
Pumpups and 2-Terminality | p. 35 |
Terminality | p. 37 |
Semirigidity | p. 38 |
Preuniqueness Subgroups | p. 43 |
Signalizer Functors and Balance | p. 48 |
Ordinary Character Theory | p. 48 |
Modular Character Theory | p. 51 |
BN-Pairs | p. 56 |
Number Theory | p. 58 |
Miscellaneous | p. 58 |
Theorem [characters not reproducible]: Stage 1 | p. 61 |
Introduction | p. 61 |
The 2-Rank 2 Case: Alperin's Theorem | p. 64 |
Theorem 2: 2-Terminal 2-Components of 2-Rank 1 | p. 67 |
The Fusion of z and Structure of Q | p. 67 |
Involutory f-Automorphisms | p. 71 |
Elimination of f-Automorphisms | p. 75 |
Theorem 3: The Nonfused Case | p. 77 |
Theorem 3: The Fused Case | p. 80 |
Theorem 4: 2-Terminal 2-Components of 2-Rank [greater than or equal] 2 | p. 86 |
The O'N Case | p. 90 |
Theorem 5 | p. 93 |
Groups of 2-Rank 3 | p. 94 |
2-Groups of Type M[subscript 12] | p. 99 |
The Proof of Theorem 6 | p. 102 |
Theorem [characters not reproducible]: Stage 2 | p. 105 |
Introduction | p. 105 |
The Structure of Involution Centralizers | p. 107 |
Other K-Subgroups of G | p. 113 |
Odd Order Signalizers | p. 117 |
An Equivariant K[superscript infinity]-Theorem | p. 123 |
Theorem 1: Uniqueness Properties of M | p. 126 |
Theorem 1: The Case m[subscript 2](S) [greater than or equal] 3 | p. 131 |
Theorem 1: The Case m[subscript 2](S) = 2 | p. 133 |
Theorems 2 and 3: Normalizers of z-Invariant Subgroups of O[subscript p](M) | p. 135 |
Theorem 2: {2, p}-Uniqueness Properties of M | p. 143 |
Theorem 2: Reduction to the Ly Case | p. 146 |
Theorem 2: The Ly Case | p. 148 |
Theorem 3: The 2-Rank 2 Case | p. 150 |
The Identification of L[subscript 3](q) | p. 157 |
Reduction to L[subscript 3](q)-Levi Form | p. 160 |
The L[subscript 3](q)-Levi Form Case | p. 164 |
Theorems 4 and 5: The Structure of M | p. 165 |
Theorems 4 and 5: Uniqueness Properties of M | p. 167 |
The Strong B-Property | p. 172 |
Theorem 6 | p. 173 |
Theorem [characters not reproducible]: Stage 3 | p. 181 |
Introduction | p. 181 |
Theorem 1: The Embedding of F | p. 183 |
Character Theory for the Dihedral Case | p. 188 |
Coherence | p. 190 |
The Case [vertical bar S vertical bar greater than or equal] 8 | p. 194 |
Theorem BG[subscript 2]: The Case [vertical bar S vertical bar greater than or equal] 8 | p. 200 |
Character Theory for the Case [vertical bar S vertical bar] = 4 | p. 203 |
Elimination of the Extruded Case | p. 208 |
The Identification of A[subscript 7] | p. 217 |
The Identification of L[subscript 2](7) and A[subscript 6] | p. 221 |
Reduction to the Brauer-Suzuki-Wall Case | p. 223 |
The Identification of L[subscript 2](q) | p. 224 |
Theorem 3: The Case M = QS | p. 230 |
Theorem 3: The Structure of C | p. 233 |
Theorem 3: The Final Contradiction | p. 240 |
Theorem 4: Local Analysis | p. 245 |
Regularity and [vertical bar G vertical bar]: Stage 1 | p. 252 |
Regularity: The Case B [not equal] 1 | p. 259 |
Regularity: The Case Q = 1 | p. 264 |
G [approximate] U[subscript 3](q) | p. 266 |
Theorem [characters not reproducible]: Stage 4 | p. 273 |
Introduction | p. 273 |
Theorem 1: Field Automorphisms | p. 275 |
The Characteristic of K | p. 286 |
G [approximate superscript 2]G[subscript 2](q) | p. 290 |
Theorem 2: The Weyl Group | p. 293 |
Theorem 2: The Torally Singular Case | p. 297 |
Theorem 2: The Case q = 3[superscript n greater than sign] 9 | p. 300 |
Theorem 2: The Case q = 9 | p. 304 |
Theorem 3: The Structure of a Sylow p-Subgroup of G | p. 309 |
The (B, N)-Pair Structure of G | p. 313 |
The Commutator Relations | p. 314 |
The Action of K[subscript 1]H | p. 318 |
The Isomorphism Type of G | p. 321 |
Theorem [characters not reproducible]: Stage 5 | p. 325 |
Introduction | p. 325 |
Theorem Sp: 2-Local Structure | p. 325 |
The p-Locals of G | p. 328 |
The Identification of PSp[subscript 4](q) | p. 332 |
SL[subscript 4 superscript plus or minus 1](q)-Amalgams | p. 333 |
Theorem LU: Local Structure | p. 340 |
Theorem LU: The General Case | p. 343 |
Theorem LU: The L[subscript 4](5) Case | p. 344 |
Theorem [characters not reproducible]: Stage 1 | p. 349 |
Introduction | p. 349 |
Theorem 1 | p. 353 |
Theorems 2 and 3 | p. 354 |
Terminally Unbalancing Triples | p. 356 |
Theorem 4: Balance with Respect to Elements of [epsilon subscript *](G) | p. 364 |
Theorem 5: L[subscript 2](G) [subset equals] [characters not reproducible] | p. 366 |
Theorem 5 | p. 372 |
Theorem 6 | p. 378 |
Theorem 7 | p. 382 |
Theorem [characters not reproducible]: Stages 2 and 3 | p. 389 |
Introduction | p. 389 |
Theorem 1: The L[subscript 3](4) Case | p. 392 |
Theorem 1: The L[subscript 2](q), A[subscript 7] Cases | p. 394 |
Fusion in the A[subscript n] Cases | p. 401 |
Theorem 2: Elements of V[subscript 2 superscript *](G) | p. 408 |
The Level of Balance | p. 413 |
Signalizer Functors | p. 424 |
The L-Preuniqueness of M | p. 432 |
Theorems 3 and 4: Reductions | p. 440 |
The L[subscript 3](4) Case | p. 443 |
G [approximate] A[subscript n] | p. 444 |
Theorem [characters not reproducible]: Stage 3 | p. 446 |
IV[subscript K]: Preliminary Properties of K-Groups | p. 451 |
The Groups L[subscript 2](q) and A[subscript 7] | p. 451 |
The Groups L[subscript 3](4) and U[subscript 3](4) | p. 462 |
Product Structures | p. 467 |
Other Groups of Lie Type | p. 471 |
Alternating Groups and Some Sporadic Groups | p. 477 |
Generation of K-Groups | p. 480 |
Pumpups | p. 484 |
2-Signalizers and p-Stability | p. 494 |
K-Groups with Prescribed Local Subgroups | p. 509 |
Signalizers and Balance | p. 512 |
Representations | p. 515 |
Background References | p. 519 |
Expository References | p. 521 |
Glossary | p. 523 |
Index | p. 527 |
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