**Proceedings of Symposia in Pure Mathematics**

Volume: 37;
1981;
634 pp;
Hardcover

MSC: Primary 20;

**Print ISBN: 978-0-8218-1440-6
Product Code: PSPUM/37**

List Price: $84.00

AMS Member Price: $67.20

MAA Member Price: $75.60

**Electronic ISBN: 978-0-8218-9326-5
Product Code: PSPUM/37.E**

List Price: $79.00

AMS Member Price: $63.20

MAA Member Price: $71.10

# The Santa Cruz Conference on Finite Groups

Share this page *Edited by *
*Bruce Cooperstein; Geoffrey Mason*

# Table of Contents

## The Santa Cruz Conference on Finite Groups

- Table of Contents v6 free
- Preface xiii14 free
- List of Participants xv16 free
- Part I: Classification theory of finite simple groups 120 free
- An outline of the classification of finite simple groups 322
- Groups of characteristic 2-type 2948
- Aschbacher blocks 3756
- Some results on standard blocks 4362
- Signalizer functors in groups of characteristic 2 type 4766
- The B-conjecture: 2-components in finite simple groups 5776
- The maximal 2-component approach to the B(G) conjecture 6786
- Finite groups having an involution centralizer with a 2-component of dihedral type 7190
- On Chevalley groups over fields of odd order, the unbalanced group conjecture and the B(G)-conjecture 7594
- Remarks on certain standard component problems and the unbalanced group conjecture 81100
- Odd standard components 85104
- Standard subgroups of Chevalley type of rank 2 and characteristic 2 91110
- Standard subgroups of type G[sub(2)](3) 95114
- Open standard form problems 99118
- Groups generated by a conjugacy class of involutions 103122
- The classification of finite groups with large extraspecial 2-subgroups 111130
- Some characterization theorems 121140
- On finite groups whose Sylow 2-subgroups are contained in unique maximal subgroups 123142
- Groups having a selfcentralizing elementary abelian subgroup of order 16 127146
- p-local subgroups 131150
- Local analysis in the odd order paper 137156
- Finite groups with a split BN-pair of rank one 139158
- Finite groups of low 2-rank, revisited 149168
- Quasithin groups 155174

- Part II: General theory of groups 159178
- Zusammengesetzte Gruppen: Hölders Programm heute 161180
- Some consequences of the classification of finite simple groups 175194
- Graphs, singularities, and finite groups 183202
- Works on finite group theory by some Chinese mathematicians 187206
- The prime graph components of finite groups 195214
- π-solvability and nilpotent Hall subgroups 197216
- On maximal subgroups with a nilpotent subgroup of index 2 201220
- Automorphisms of nilpotent groups and supersolvable orders 205224
- A short survey of Fitting classes 209228
- Transfer theorems 213232
- Problem areas in infinite group theory for finite group theorists 217236
- Classification theorems for torsionfree groups 225244

- Part III: Properties of the known groups 229248
- Properties of the known simple groups 231250
- The root groups of a maximal torus 239258
- Geometry of long root subgroups in groups of Lie type 243262
- S and F-pairs for groups of Lie type in characteristic two 249268
- Geometric questions arising in the study of unipotent elements 255274
- Kleinian singularities and unipotent elements 265284
- The construction of J[sub(4)] 271290
- Schur multipliers of the known finite simple groups. II 279298
- 2-local geometries for some sporadic groups 283302

- Part IV: Representation theory of groups of Lie-type 291310
- Problems concerning characters of finite groups of Lie type 293312
- The relation between characteristic 0 representations and characteristic p representations of finite groups of Lie type 301320
- Some problems in the representation theory of finite Chevalley groups 313332
- Representations in characteristic p 319338
- Characters of finite groups of Lie type. II 333352
- Principal series representations of finite groups with split (BN)-pairs 341360
- Cartan invariants and decomposition numbers of Chevalley groups 347366
- Duality in the character ring of a finite Chevalley group 353372
- Characters of projective indecomposable modules for finite Chevalley groups 359378
- Some indecomposable modules of groups with split (B, N)-pairs 363382

- Part V: Character theory of finite groups 367386
- Local representation theory 369388
- Characters of solvable groups 377396
- Local block theory in p-solvable groups 385404
- Characters of finite π-separable groups 389408
- On characters of height zero 393412
- Brauer trees and character degrees 397416
- A correspondence of characters 401420
- Irreducible modules for p-solvable groups 405424
- Finite complex linear groups of degree less than (2q+ l)/3 413432
- A criterion for cyclicity 419438
- A characterization of generalized permutation characters 423442
- Character tables, trivial intersections and number of involutions 425444
- Representation theory and solvable groups: Length type problems 431450

- Part VI: Combinatorics 443462
- Group problems arising from combinatorics 445464
- Group-related geometries 457476
- Near n-gons 461480
- Orthogonal polynomials, algebraic combinatorics and spherical t-designs 465484
- Finite translation planes and group representation 469488
- Finite collineation groups of projective planes containing nontrivial perspectivities 473492
- Further problems concerning finite geometries and finite groups 479498

- Part VII: Computer applications 485504
- Part VIII: Connections with number theory and other fields 519538
- Modular functions 521540
- A finiteness theorem for subgroups of PSL(2, R) which are comensurable with PSL(2, Z) 533552
- Characters arising in the monster-modular connection 557576
- Modular functions and finite simple groups 561580
- Euclidean Lie algebras and the modular function j 567586
- Exposition on an arithmetic-group theoretic connection via Riemann's existence theorem 571590
- Burnside ring of a Galois group and the relations between zeta functions of intermediate fields 603622
- Finite automorphism groups of algebraic varieties 611630
- Transformation groups and representation theory 621640
- Lie algebras with nilpotent centralizers 633652