The Santa Cruz Conference on Finite Groups

Cover......Page 1
The Santa Cruz Conference on Finite Groups......Page 2
Copyright Page......Page 3
Table of Contents......Page 4
Preface......Page 12
List of Participants......Page 14
I. Classification theory of finite simple groups......Page 18
Gorenstein: An outline of the classification of finite simple groups......Page 20
Aschbacher: Groups of characteristic 2-type......Page 46
Foote: Aschbacher blocks......Page 54
Solomon: Some results on standard blocks......Page 60
Lyons: Signalizer functors in groups of characteristic 2 type......Page 64
Walter: The B-conjecture: 2-components in finite simple groups......Page 74
Solomon: The maximal 2-component approach to the B(G) conjecture......Page 84
Harris: Finite groups having an involution centralizer with a 2-component of dihedral type......Page 88
Harris: On Chevalley groups over fields of odd order, the unbalanced group conjecture and the B(G)-conjecture......Page 92
Gomi: Remarks on certain standard component problems and the unbalanced group conjecture......Page 98
Gilman: Odd standard components......Page 102
Miyamoto: Standard subgroups of Chevalley type of rank 2 and characteristic 2......Page 108
Yamada: Standard subgroups of type G2(3)......Page 112
Finkelstein: Open standard form problems......Page 116
Timmesfeld: Groups generated by a conjugacy class of involutions......Page 120
Smith: The classification of finite groups with large extraspecial 2-subgroups......Page 128
Syskin: Some characterization theorems......Page 138
Stellmacher: On finite groups whose Sylow 2-subgroups are contained in unique maximal subgroups......Page 140
Stroth: Groups having a selfcentralizing elementary abelian subgroup of order 16......Page 144
Glauberman: p-local subgroups......Page 148
Glauberman: Local analysis in the odd order paper......Page 154
Suzuki: Finite groups with a split BN-pair of rank one......Page 156
Harada: Finite groups of low 2-rank, revisited......Page 166
Mason: Quasithin groups......Page 172
II. General theory of groups......Page 176
Wielandt: Zusammengesetzte Gruppen: H鰈ders Programm heute......Page 178
Feit: Some consequences of the classification of finite simple groups......Page 192
McKay: Graphs, singularities, and finite groups......Page 200
Tuan: Works on finite group theory by some Chinese mathematicians......Page 204
Williams: The prime graph components of finite groups......Page 212
Arad & Chillag: π-solvability and nilpotent Hall subgroups......Page 214
Arad, Herzog & Shaki: On maximal subgroups with a nilpotent subgroup of index 2......Page 218
Hughes: Automorphisms of nilpotent groups and supersolvable orders......Page 222
Camina: A short survey of Fitting classes......Page 226
Yoshida: Transfer theorems......Page 230
Baumslag: Problem areas in infinite group theory for finite group theorists......Page 234
Kov醕s: Classification theorems for torsionfree groups......Page 242
III. Properties of the known groups......Page 246
Seitz: Properties of the known simple groups......Page 248
Seitz: The root groups of a maximal torus......Page 256
Cooperstein: Geometry of long root subgroups in groups of Lie type......Page 260
Cooperstein: S and F-pairs for groups of Lie type in characteristic two......Page 266
Springer: Geometric questions arising in the study of unipotent elements......Page 272
Steinberg: Kleinian singularities and unipotent elements......Page 282
Norton: The construction of J4......Page 288
Griess: Schur multipliers of the known finite simple groups II......Page 296
Ronan & Smith: 2-local geometries for some sporadic groups......Page 300
IV. Representation theory of groups of Lie-type......Page 308
Curtis: Problems concerning characters of finite groups of Lie type......Page 310
Carter: The relation between characteristic 0 representations and characteristic p representations of finite groups of Lie type......Page 318
Lusztig: Some problems in the representation theory of finite Chevalley groups......Page 330
Scott: Representations in characteristic p......Page 336
Srinivasan: Characters of finite groups of Lie type II......Page 350
Kilmoyer: Principal series representations of finite groups with split (B,N)-pairs......Page 358
Humphreys: Cartan invariants and decomposition numbers of Chevalley groups......Page 364
Alvis: Duality in the character ring of a finite Chevalley group......Page 370
Chastkofsky: Characters of projective modules for finite Chevalley groups......Page 376
Tinberg: Some indecomposable modules of groups with split (B,N)-pairs......Page 380
V. Character theory of finite groups......Page 384
Alperin: Local representation theory......Page 386
Isaacs: Characters of solvable groups......Page 394
Puig: Local block theory in p-solvable groups......Page 402
Gajendragadkar: Characters of finite π-separable groups......Page 406
Brou? On characters of height zero......Page 410
Blau: Brauer trees and character degrees......Page 414
Dade: A correspondence of characters......Page 418
Feit: Irreducible modules of p-solvable groups......Page 422
Ferguson: Finite complex linear groups of degree less than (2q+1)/3......Page 430
Landrock & Michler: A criterion for cyclicity......Page 436
Gluck: A characterization of generalized permutation characters......Page 440
Herzog: Character tables, trivial intersections and number of involutions......Page 442
Berger: Representation theory of solvable groups: length type problems......Page 448
VI. Combinatorics......Page 460
Hall: Group problems arising from combinatorics......Page 462
Shult: Group-related geometries......Page 474
Shad & Shult: Near n-gons......Page 478
Bannai: Orthogonal polynomials, algebraic combinatorics and spherical t-designs......Page 482
Ostrom: Finite translation planes and group representation......Page 486
Hering: Finite collineation groups of projective planes containing nontrivial perspectivities......Page 490
Kantor: Further problems concerning finite geometries and finite groups......Page 496
VII. Computer applications......Page 502
Cannon: Effective procedures for the recognition of primitive groups......Page 504
Cannon: Software tools for group theory......Page 512
Felsch: The computation of a counterexample to the class-breadth conjecture for p-groups......Page 520
Hunt: A computer-based atlas of finite simple groups......Page 524
Leon: Finding the order of a permutation group......Page 528
VIII. Connections with number theory and other fields......Page 536
Ogg: Modular functions......Page 538
Thompson: A finiteness theorem for subgroups of PSL(2,R) which are commensurable with PSL(2,Z)......Page 550
Fong: Characters arising in the monster-modular connection......Page 574
Queen: Modular functions and finite simple groups......Page 578
Lepowski: Euclidean Lie algebras and the modular function j......Page 584
Fried: Exposition on an arithmetic-group theoretic connection via Riemann's existence theorem......Page 588
Husemoller: Burnside ring of a Galois group and the relations between zeta functions of intermediate fields......Page 620
Husemoller: Finite automorphism groups of algebraic varieties......Page 628
Petrie: Transformation groups and representation theory......Page 638
Isaacs: Lie algebras with nilpotent centralizers......Page 650