Groups of Lie Type and their Geometries

doi:10.1017/CBO9780511565823

Presented here are papers from the 1993 Como meeting on groups of Lie type and their geometries. The meeting was attended by many leading figures, as well as younger researchers in this area, and this book brings together many of their excellent contributions. Themes represented here include: subgroups of finite and algebraic groups; buildings and other geometries associated to groups of Lie type or Coxeter groups; generation and applications. This book will be a necessary addition to the library of all researchers in group theory and related areas.

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Contents

Frontmatter
pp i-iv
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Contents
pp v-vi
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Preface
pp vii-viii
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List of talks
pp ix-x
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List of participants
pp xi-xiv
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Representations of groups on finite simplicial complexes
pp 1-12
- By Michael Aschbacher, California Institute of Technology
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Coxeter groups and matroids
pp 13-34
- By Alexandre V. Borovik, K. Sian Roberts, Department of Mathematics, UMIST PO Box 88, Manchester M60 1QD United Kingdom
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Finite groups and geometries: A view on the present state and on the future
pp 35-42
- By Francis Buekenhout, Université Libre de Bruxelles Campus Plaine C.P.216 Bd du Triomphe B-1050 Bruxelles
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Groups acting simply transitively on the vertices of a building of type Ãn
pp 43-76
- By Donald I. Cartwright
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Finite simple subgroups of semisimple complex Lie groups – a survey
pp 77-96
- By Arjeh M. Cohen, Fac. Wisk. en Inf. TUE P.O. Box 513 5600 MB Eindhoven The Netherlands, David B. Wales, Sloan Lab Caltech Pasadena CA 91125 USA
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Flag-transitive extensions of buildings of type G2 and C3*
pp 97-110
- By Hans Cuypers
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Disconnected linear groups and restrictions of representations
pp 111-116
- By Ben Ford
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Products of conjugacy classes in algebraic groups and generators of dense subgroups
pp 117-124
- By Nikolai L. Gordeev
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Monodromy groups of polynomials
pp 125-150
- By Robert M. Guralnick, Jan Saxl
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Subgroups of exceptional algebraic groups
pp 151-156
- By Martin W. Liebeck, Gary M. Seitz
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The geometry of traces in Ree octagons
pp 157-172
- By H. Van Maldeghem
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Small rank exceptional Hurwitz groups
pp 173-184
- By Gunter Malle, Mathematisches Institut und IWR, Im Neuenheimer Feld 368, D - 69120 Heidelberg.
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The direct sum problem for chamber systems
pp 185-214
- By Antonio Pasini
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Embeddings and hyperplanes of Lie incidence geometries
pp 215-232
- By Ernest E. Shult
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Intermediate subgroups in Chevalley groups
pp 233-280
- By Nikolai Vavilov, Department of Mathematics and Mechanics University of Sanct-Petersburg Petrodvorets, 198904, Russia and Fakultāt für Mathematik Universitāt Bielefeld 33615, Bielefeld, Deutschland
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On a certain class of Frattini extensions of finite Chevalley groups
pp 281-288
- By Thomas Weigel
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Economical generating sets for finite simple groups
pp 289-306
- By John S. Wilson
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Groups of Lie Type and their Geometries

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-viii

List of talks
pp ix-x

List of participants
pp xi-xiv

Representations of groups on finite simplicial complexes
pp 1-12

Coxeter groups and matroids
pp 13-34

Finite groups and geometries: A view on the present state and on the future
pp 35-42

Groups acting simply transitively on the vertices of a building of type Ãn
pp 43-76

Finite simple subgroups of semisimple complex Lie groups – a survey
pp 77-96

Flag-transitive extensions of buildings of type G2 and C3*
pp 97-110

Disconnected linear groups and restrictions of representations
pp 111-116

Products of conjugacy classes in algebraic groups and generators of dense subgroups
pp 117-124

Monodromy groups of polynomials
pp 125-150

Subgroups of exceptional algebraic groups
pp 151-156

The geometry of traces in Ree octagons
pp 157-172

Small rank exceptional Hurwitz groups
pp 173-184

The direct sum problem for chamber systems
pp 185-214

Embeddings and hyperplanes of Lie incidence geometries
pp 215-232

Intermediate subgroups in Chevalley groups
pp 233-280

On a certain class of Frattini extensions of finite Chevalley groups
pp 281-288

Economical generating sets for finite simple groups
pp 289-306

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Groups of Lie Type and their Geometries

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