Some theory of linear algebraic groups |
The finite groups of Lie type |
Local subgroups of groups of Lie type I |
Local subgroups of groups of Lie type II |
The alternating groups and the twenty-six sporadic groups |
Coverings and embeddings of quasisimple $\mathcal {K}$-groups |
General properties of $\mathcal {K}$-groups Background |
References Expository |
References Errata for numbers 1 and 2 |
Glossary |
Index |
Chapters 1-4: Uniqueness Theorems / Part II: |
General lemmas Strongly embedded subgroups and related |
Conditions On Involutions $P$-Component Uniqueness Theorems |
Properties of $K$-groups Background |
References Errata for number 3, Chapter I$_A$: Almost simple $\mathcal K$-groups |
Index of terminology |
Theorem $C_7$: General Introduction |
General group-theoretic results |
Theorem $C^*_7$: Stage 1 |
Theorem $C^*_7$: Stage 2 |
Theorem $C^*_7$: Stage 3a |
Properties of $K$-groups |
Background |
References |
Glossary of symbols and terms |
Preface |
The Special Odd Case / Part IV: |
General Introduction to the Special Odd Case / Chapter 1: |
The Goals: Theorems [characters not reproducible] and [characters not reproducible] / 1: |
Theorems [characters not reproducible] and [characters not reproducible] / 2: |
General Comments on the Proof of Theorem [characters not reproducible] / 3: |
Theorem [characters not reproducible] and Its Proof / 4: |
General Lemmas / Chapter 2: |
The Bender/Glauberman Method |
p-Groups and Coprime Action |
Transfer and Fusion |
2-Components and 2-Groups |
Pumpups and 2-Terminality / 5: |
Terminality / 6: |
Semirigidity / 7: |
Preuniqueness Subgroups / 8: |
Signalizer Functors and Balance / 9: |
Ordinary Character Theory / 10: |
Modular Character Theory / 11: |
BN-Pairs / 12: |
Number Theory / 13: |
Miscellaneous / 14: |
Theorem [characters not reproducible]: Stage 1 / Chapter 3: |
Introduction |
The 2-Rank 2 Case: Alperin's Theorem |
Theorem 2: 2-Terminal 2-Components of 2-Rank 1 |
The Fusion of z and Structure of Q |
Involutory f-Automorphisms |
Elimination of f-Automorphisms |
Theorem 3: The Nonfused Case |
Theorem 3: The Fused Case |
Theorem 4: 2-Terminal 2-Components of 2-Rank [greater than or equal] 2 |
The O'N Case |
Theorem 5 |
Groups of 2-Rank 3 |
2-Groups of Type M[subscript 12] |
The Proof of Theorem 6 |
Theorem [characters not reproducible]: Stage 2 / Chapter 4: |
The Structure of Involution Centralizers |
Other K-Subgroups of G |
Odd Order Signalizers |
An Equivariant K[superscript infinity]-Theorem |
Theorem 1: Uniqueness Properties of M |
Theorem 1: The Case m[subscript 2](S) [greater than or equal] 3 |
Theorem 1: The Case m[subscript 2](S) = 2 |
Theorems 2 and 3: Normalizers of z-Invariant Subgroups of O[subscript p](M) |
Theorem 2: {2, p}-Uniqueness Properties of M |
Theorem 2: Reduction to the Ly Case |
Theorem 2: The Ly Case |
Theorem 3: The 2-Rank 2 Case |
The Identification of L[subscript 3](q) |
Reduction to L[subscript 3](q)-Levi Form / 15: |
The L[subscript 3](q)-Levi Form Case / 16: |
Theorems 4 and 5: The Structure of M / 17: |
Theorems 4 and 5: Uniqueness Properties of M / 18: |
The Strong B-Property / 19: |
Theorem 6 / 20: |
Theorem [characters not reproducible]: Stage 3 / Chapter 5: |
Theorem 1: The Embedding of F |
Character Theory for the Dihedral Case |
Coherence |
The Case [vertical bar S vertical bar greater than or equal] 8 |
Theorem BG[subscript 2]: The Case [vertical bar S vertical bar greater than or equal] 8 |
Character Theory for the Case [vertical bar S vertical bar] = 4 |
Elimination of the Extruded Case |
The Identification of A[subscript 7] |
The Identification of L[subscript 2](7) and A[subscript 6] |
Reduction to the Brauer-Suzuki-Wall Case |
The Identification of L[subscript 2](q) |
Theorem 3: The Case M = QS |
Theorem 3: The Structure of C |
Theorem 3: The Final Contradiction |
Theorem 4: Local Analysis |
Regularity and [vertical bar G vertical bar]: Stage 1 |
Regularity: The Case B [not equal] 1 |
Regularity: The Case Q = 1 |
G [approximate] U[subscript 3](q) |
Theorem [characters not reproducible]: Stage 4 / Chapter 6: |
Theorem 1: Field Automorphisms |
The Characteristic of K |
G [approximate superscript 2]G[subscript 2](q) |
Theorem 2: The Weyl Group |
Theorem 2: The Torally Singular Case |
Theorem 2: The Case q = 3[superscript n greater than sign] 9 |
Theorem 2: The Case q = 9 |
Theorem 3: The Structure of a Sylow p-Subgroup of G |
The (B, N)-Pair Structure of G |
The Commutator Relations |
The Action of K[subscript 1]H |
The Isomorphism Type of G |
Theorem [characters not reproducible]: Stage 5 / Chapter 7: |
Theorem Sp: 2-Local Structure |
The p-Locals of G |
The Identification of PSp[subscript 4](q) |
SL[subscript 4 superscript plus or minus 1](q)-Amalgams |
Theorem LU: Local Structure |
Theorem LU: The General Case |
Theorem LU: The L[subscript 4](5) Case |
Theorem 1 / Chapter 8: |
Theorems 2 and 3 |
Terminally Unbalancing Triples |
Theorem 4: Balance with Respect to Elements of [epsilon subscript *](G) |
Theorem 5: L[subscript 2](G) [subset equals] [characters not reproducible] |
Theorem 7 |
Theorem [characters not reproducible]: Stages 2 and 3 / Chapter 9: |
Theorem 1: The L[subscript 3](4) Case |
Theorem 1: The L[subscript 2](q), A[subscript 7] Cases |
Fusion in the A[subscript n] Cases |
Theorem 2: Elements of V[subscript 2 superscript *](G) |
The Level of Balance |
Signalizer Functors |
The L-Preuniqueness of M |
Theorems 3 and 4: Reductions |
The L[subscript 3](4) Case |
G [approximate] A[subscript n] |
IV[subscript K]: Preliminary Properties of K-Groups / Chapter 10: |
The Groups L[subscript 2](q) and A[subscript 7] |
The Groups L[subscript 3](4) and U[subscript 3](4) |
Product Structures |
Other Groups of Lie Type |
Alternating Groups and Some Sporadic Groups |
Generation of K-Groups |
Pumpups |
2-Signalizers and p-Stability |
K-Groups with Prescribed Local Subgroups |
Signalizers and Balance |
Representations |
Background References |
Expository References |
Some theory of linear algebraic groups |
The finite groups of Lie type |
Local subgroups of groups of Lie type I |
Local subgroups of groups of Lie type II |
The alternating groups and the twenty-six sporadic groups |
Coverings and embeddings of quasisimple $\mathcal {K}$-groups |