The classification of quasithin groups /
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| Author / Creator: | Aschbacher, Michael, 1944- |
|---|---|
| Imprint: | Providence, R.I. : American Mathematical Society, c2004. |
| Description: | 2 v. (xiv, 1221 p.) ; 27 cm. |
| Language: | English |
| Series: | Mathematical surveys and monographs, 0076-5376 ; v. 111-112 Mathematical surveys and monographs ; no. 111-112. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/5518991 |
Table of Contents:
- Preface
- Volume I. Structure of strongly quasithin K-groups
- Introduction to Volume I
- 0.1. Statement of Main Results
- 0.2. An overview of Volume I
- 0.3. Basic results on finite groups
- 0.4. Semisimple quasithin and strongly quasithin K-groups
- 0.5. The structure of SQTK-groups
- 0.6. Thompson factorization and related notions
- 0.7. Minimal parabolics
- 0.8. Pushing up
- 0.9. Weak closure
- 0.10. The amalgam method
- 0.11. Properties of K-groups
- 0.12. Recognition theorems
- 0.13. Background References
- Chapter A. Elementary group theory and the known quasithin groups
- A.1. Some standard elementary results
- A.2. The list of quasithin K-groups: Theorems A, B, and C
- A.3. A structure theory for Strongly Quasithin K-groups
- A.4. Signalizers for groups with X = O[superscript 2] (X)
- A.5. An ordering on M(T)
- A.6. A group-order estimate
- Chapter B. Basic results related to Failure of Factorization
- B.1. Representations and FF-modules
- B.2. Basic Failure of Factorization
- B.3. The permutation module for A[subscript n] and its FF*-offenders
- B.4. F[subscript 2]-representations with small values of q or q
- B.5. FF-modules for SQTK-groups
- B.6. Minimal parabolics
- B.7. Chapter appendix: Some details from the literature
- Chapter C. Pushing-up in SQTK-groups
- C.1. Blocks and the most basic results on pushing-up
- C.2. More general pushing up in SQTK-groups
- C.3. Pushing up in nonconstrained 2-locals
- C.4. Pushing up in constrained 2-locals
- C.5. Finding a common normal subgroup
- C.6. Some further pushing up theorems
- Chapter D. The qrc-lemma and modules with q [less than or equal] 2
- D.1. Stellmacher's qrc-Lemma
- D.2. Properties of q and q: R(G, V) and Q(G, V)
- D.3. Modules with q [less than or equal] 2
- Chapter E. Generation and weak closure
- E.1. [epsilon]-generation and the parameter n(G)
- E.2. Minimal parabolics under the SQTK-hypothesis
- E.3. Weak Closure
- E.4. Values of a for F[subscript 2]-representations of SQTK-groups
- E.5. Weak closure and higher Thompson subgroups
- E.6. Lower bounds on r(G, V)
- Chapter F. Weak BN-pairs and amalgams
- F.1. Weak BN-pairs of rank 2
- F.2. Amalgams, equivalences, and automorphisms
- F.3. Paths in rank-2 amalgams
- F.4. Controlling completions of Lie amalgams
- F.5. Identifying L[subscript 4](3) via its U[subscript 4](2)-amalgam
- F.6. Goldschmidt triples
- F.7. Coset geometries and amalgam methodology
- F.8. Coset geometries with b [greater than sign] 2
- F.9. Coset geometries with b [greater than sign] 2 and m (V[subscript 1]) = 1
- Chapter G. Various representation-theoretic lemmas
- G.1. Characterizing direct sums of natural SL[subscript n](F[subscript 2 superscript e])-modules
- G.2. Almost-special groups
- G.3. Some groups generated by transvections
- G.4. Some subgroups of Sp[subscript 4](2[superscript n])
- G.5. F[subscript 2]-modules for A[subscript 6]
- G.6. Modules with m(G, V) [less than or equal] 2
- G.7. Small-degree representations for some SQTK-groups
- G.8. An extension of Thompson's dihedral lemma
- G.9. Small-degree representations for more general SQTK-groups
- G.10. Small-degree representations on extraspecial groups
- G.11. Representations on extraspecial groups for SQTK-groups
- G.12. Subgroups of Sp(V) containing transvections on hyperplanes
- Chapter H. Parameters for some modules
- H.1. [Omega superscript epsilon subscript 4](2[superscript n]) on an orthogonal module of dimension 4n (n [greater than sign] 1)
- H.2. SU[subscript 3](2[superscript n]) on a natural 6n-dimensional module
- H.3. Sz(2[superscript n]) on a natural 4n-dimensional module
- H.4. (S)L[subscript 3](2[superscript n]) on modules of dimension 6 and 9
- H.5. 7-dimensional permutation modules for L[subscript 3](2)
- H.6. The 21-dimensional permutation module for L[subscript 3](2)
- H.7. Sp[subscript 4](2[superscript n]) on natural 4n plus the conjugate 4n[superscript t]
- H.8. A[subscript 7] on 4 [plus sign in circle] 4
- H.9. Aut(L[subscript n](2)) on the natural n plus the dual n*
- H.10. A foreword on Mathieu groups
- H.11. M[subscript 12] on its 10-dimensional module
- H.12. 3M[subscript 22] on its 12-dimensional modules
- H.13. Preliminaries on the binary code and cocode modules
- H.14. Some stabilizers in Mathieu groups
- H.15. The cocode modules for the Mathieu groups
- H.16. The code modules for the Mathieu groups
- Chapter I. Statements of some quoted results
- I.1. Elementary results on cohomology
- I.2. Results on structure of nonsplit extensions
- I.3. Balance and 2-components
- I.4. Recognition Theorems
- I.5. Characterizations of L[subscript 4](2) and Sp[subscript 6](2)
- I.6. Some results on TI-sets
- I.7. Tightly embedded subgroups
- I.8. Discussion of certain results from the Bibliography
- Chapter J. A characterization of the Rudvalis group
- J.1. Groups of type Ru
- J.2. Basic properties of groups of type Ru
- J.3. The order of a group of type Ru
- J.4. A [superscript 2]F[subscript 4](2)-subgroup
- J.5. Identifying G as Ru
- Chapter K. Modules for SQTK-groups with q(G, V) [less than or equal] 2
- Notation and overview of the approach
- K.1. Alternating groups
- K.2. Groups of Lie type and odd characteristic
- K.3. Groups of Lie type and characteristic 2
- K.4. Sporadic groups
- Bibliography and Index
- Background References Quoted (Part 1: also used by GLS)
- Background References Quoted (Part 2: used by us but not by GLS)
- Expository References Mentioned
- Index
