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The Santa Cruz Conference on Finite Groups

About this Title

Bruce Cooperstein and Geoffrey Mason, Editors

Publication: Proceedings of Symposia in Pure Mathematics
Publication Year: 1981; Volume 37
ISBNs: 978-0-8218-1440-6 (print); 978-0-8218-9326-5 (online)
DOI: https://doi.org/10.1090/pspum/037

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Table of Contents

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Front/Back Matter

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Part I: Classification theory of simple finite groups

• Daniel Gorenstein – An outline of the classification of finite simple groups [MR 604552]
• Michael Aschbacher – Groups of characteristic $2$-type [MR 604553]
• Richard Foote – Aschbacher blocks [MR 604554]
• Ronald Solomon – Some results on standard blocks [MR 604555]
• Richard Lyons – Signalizer functors in groups of characteristic $2$ type [MR 604556]
• John H. Walter – The $B$-conjecture: $2$-components in finite simple groups [MR 604557]
• Ronald Solomon – The maximal $2$-component approach to the $B(G)$ conjecture [MR 604558]
• Morton E. Harris – Finite groups having an involution centralizer with a $2$-component of dihedral type [MR 604559]
• Morton E. Harris – On Chevalley groups over fields of odd order, the unbalanced group conjecture and the $B(G)$-conjecture [MR 604560]
• Kensaku Gomi – Remarks on certain standard component problems and the unbalanced group conjecture [MR 604561]
• Robert Gilman – Odd standard components [MR 604562]
• Izumi Miyamoto – Standard subgroups of Chevalley type of rank $2$ and characteristic $2$ [MR 604563]
• Hiromichi Yamada – Standard subgroups of type $G_{2}(3)$ [MR 604564]
• Larry Finkelstein – Open standard form problems [MR 604565]
• F. Timmesfeld – Groups generated by a conjugacy class of involutions [MR 604566]
• Stephen D. Smith – The classification of finite groups with large extraspecial $2$-subgroups [MR 604567]
• Sergei Syskin, A. – Some characterization theorems [MR 604568]
• Bernd Stellmacher – On finite groups whose Sylow $2$-subgroups are contained in unique maximal subgroups [MR 604569]
• G. Stroth – Groups having a self-centralizing elementary abelian subgroup of order $16$ [MR 604570]
• George Glauberman – $p$-local subgroups [MR 604571]
• George Glauberman – Local analysis in the odd order paper
• Michio Suzuki – Finite groups with a split $BN$-pair of rank one [MR 604572]
• Koichiro Harada – Finite groups of low $2$-rank, revisited [MR 604573]
• Geoffrey Mason – Quasithin groups [MR 604574]

Part II: General theory of groups

• Helmut Wielandt – Zusammengesetzte Gruppen: Hölders Programm heute [MR 604575]
• Walter Feit – Some consequences of the classification of finite simple groups [MR 604576]
• John McKay – Graphs, singularities, and finite groups [MR 604577]
• Hsio Fu Tuan – Works on finite group theory by some Chinese mathematicians [MR 604578]
• J. S. Williams – The prime graph components of finite groups [MR 604579]
• Zvi Arad and David Chillag – $\pi$-solvability and nilpotent Hall subgroups [MR 604580]
• Zvi Arad, Marcel Herzog and Ahiezer Shaki – On maximal subgroups with a nilpotent subgroup of index $2$ [MR 604581]
• Anthony Hughes – Automorphisms of nilpotent groups and supersolvable orders [MR 604582]
• A. R. Camina – A short survey of Fitting classes [MR 604583]
• Tomoyuki Yoshida – Transfer theorems [MR 604584]
• Gilbert Baumslag – Problem areas in infinite group theory for finite group theorists [MR 604585]
• L. G. Kovács – Classification theorems for torsion-free groups [MR 604586]

Part III: Properties of the known groups

• Gary M. Seitz – Properties of the known simple groups [MR 604587]
• Gary M. Seitz – The root groups of a maximal torus [MR 604588]
• B. Cooperstein – Geometry of long root subgroups in groups of Lie type [MR 604589]
• B. Cooperstein – $S$- and $F$-pairs for groups of Lie type in characteristic two [MR 604590]
• T. A. Springer – Geometric questions arising in the study of unipotent elements [MR 604591]
• Robert Steinberg – Kleinian singularities and unipotent elements [MR 604592]
• Simon Norton – The construction of $J_{4}$ [MR 604593]
• Robert L. Griess, Jr. – Schur multipliers of the known finite simple groups. II [MR 604594]
• M. A. Ronan and S. D. Smith – $2$-local geometries for some sporadic groups [MR 604595]

Part IV: Representation theory of groups of Lie-type

• Charles W. Curtis – Problems concerning characters of finite groups of Lie type [MR 604596]
• R. W. Carter – The relation between characteristic $0$ representations and characteristic $p$ representations of finite groups of Lie type [MR 604597]
• George Lusztig – Some problems in the representation theory of finite Chevalley groups [MR 604598]
• Leonard L. Scott – Representations in characteristic $p$ [MR 604599]
• Bhama Srinivasan – Characters of finite groups of Lie type. II [MR 604600]
• R. W. Kilmoyer – Principal series representations of finite groups with split $(BN)$-pairs [MR 604601]
• J. E. Humphreys – Cartan invariants and decomposition numbers of Chevalley groups [MR 604602]
• Dean Alvis – Duality in the character ring of a finite Chevalley group [MR 604603]
• Leonard Chastkofsky – Characters of projective indecomposable modules for finite Chevalley groups [MR 604604]
• N. B. Tinberg – Some indecomposable modules of groups with split $(B,\,N)$-pairs [MR 604605]

Part V: Character theory of finite groups

• J. L. Alperin – Local representation theory [MR 604606]
• I. M. Isaacs – Characters of solvable groups [MR 604607]
• Lluís Puig – Local block theory in $p$-solvable groups [MR 604608]
• Dilip Gajendragadkar – Characters of finite $\pi$-separable groups [MR 604609]
• Michel Broué – On characters of height zero [MR 604610]
• Harvey I. Blau – Brauer trees and character degrees [MR 604611]
• Everett C. Dade – A correspondence of characters [MR 604612]
• Walter Feit – Irreducible modules of $p$-solvable groups [MR 604613]
• Pamela A. Ferguson – Finite complex linear groups of degree less than $(2q+1)/3$ [MR 604614]
• Peter Landrock and Gerhard O. Michler – A criterion for cyclicity [MR 604615]
• David Gluck – A characterization of generalized permutation characters [MR 604616]
• Marcel Herzog – Character tables, trivial intersections and number of involutions [MR 604617]
• T. R. Berger – Representation theory and solvable groups: length type problems [MR 604618]

Part VI: Combinatorics

• Marshall Hall, Jr. – Group problems arising from combinatorics [MR 604619]
• Ernest Shult – Group-related geometries [MR 604620]
• Saeed Shad and Ernest Shult – Near $n$-gons [MR 604621]
• Eiichi Bannai – Orthogonal polynomials, algebraic combinatorics and spherical $t$-designs [MR 604622]
• T. G. Ostrom – Finite translation planes and group representation [MR 604623]
• Christoph Hering – Finite collineation groups of projective planes containing nontrivial perspectivities [MR 604624]
• William M. Kantor – Further problems concerning finite geometries and finite groups [MR 604625]

Part VII: Computer applications

• John J. Cannon – Effective procedures for the recognition of primitive groups [MR 604626]
• John J. Cannon – Software tools for group theory [MR 604627]
• Volkmar Felsch – The computation of a counterexample to the class-breadth conjecture for $p$-groups [MR 604628]
• David C. Hunt – A computer-based atlas of finite simple groups [MR 604629]
• Jeffrey S. Leon – Finding the order of a permutation group [MR 604630]

Part VIII: Connections with number theory and other fields

• A. P. Ogg – Modular functions [MR 604631]
• J. G. Thompson – A finiteness theorem for subgroups of $\mathrm {PSL}(2,\,\mathbf {R})$ which are commensurable with $\mathrm {PSL}(2,\,\mathbf {Z})$ [MR 604632]
• Paul Fong – Characters arising in the Monster-modular connection [MR 604633]
• Larissa Queen – Modular functions and finite simple groups [MR 604634]
• J. Lepowsky – Euclidean Lie algebras and the modular function $j$ [MR 604635]
• M. Fried – Exposition on an arithmetic-group theoretic connection via Riemann’s existence theorem [MR 604636]
• D. Husemoller – Burnside ring of a Galois group and the relations between zeta functions of intermediate fields [MR 604637]
• D. Husemoller – Finite automorphism groups of algebraic varieties [MR 604638]
• Ted Petrie – Transformation groups and representation theory [MR 604639]
• I. M. Isaacs – Lie algebras with nilpotent centralizers [MR 604640]