Book contents
- Frontmatter
- Contents
- Preface
- List of talks
- List of participants
- Representations of groups on finite simplicial complexes
- Coxeter groups and matroids
- Finite groups and geometries: A view on the present state and on the future
- Groups acting simply transitively on the vertices of a building of type Ãn
- Finite simple subgroups of semisimple complex Lie groups – a survey
- Flag-transitive extensions of buildings of type G2 and C3*
- Disconnected linear groups and restrictions of representations
- Products of conjugacy classes in algebraic groups and generators of dense subgroups
- Monodromy groups of polynomials
- Subgroups of exceptional algebraic groups
- The geometry of traces in Ree octagons
- Small rank exceptional Hurwitz groups
- The direct sum problem for chamber systems
- Embeddings and hyperplanes of Lie incidence geometries
- Intermediate subgroups in Chevalley groups
- On a certain class of Frattini extensions of finite Chevalley groups
- Economical generating sets for finite simple groups
Representations of groups on finite simplicial complexes
Published online by Cambridge University Press: 06 January 2010
- Frontmatter
- Contents
- Preface
- List of talks
- List of participants
- Representations of groups on finite simplicial complexes
- Coxeter groups and matroids
- Finite groups and geometries: A view on the present state and on the future
- Groups acting simply transitively on the vertices of a building of type Ãn
- Finite simple subgroups of semisimple complex Lie groups – a survey
- Flag-transitive extensions of buildings of type G2 and C3*
- Disconnected linear groups and restrictions of representations
- Products of conjugacy classes in algebraic groups and generators of dense subgroups
- Monodromy groups of polynomials
- Subgroups of exceptional algebraic groups
- The geometry of traces in Ree octagons
- Small rank exceptional Hurwitz groups
- The direct sum problem for chamber systems
- Embeddings and hyperplanes of Lie incidence geometries
- Intermediate subgroups in Chevalley groups
- On a certain class of Frattini extensions of finite Chevalley groups
- Economical generating sets for finite simple groups
Summary
Until recently there have been relatively few articles in the finite group theoretic literature on representations of finite groups on simplicial complexes. However in the last few years that situation has begun to change. This paper discusses some of the activity in the area. We begin with a fairly general discussion intended to give a feeling for the kind of activity now going on. Since space is limited, we touch on only a few examples of such activity, and to provide focus, we eventually concentrate on p-group complexes of finite groups. In the end we concentrate even further on a particular problem in the area of p-group complexes: the question of when p-group complexes of finite groups are simply connected. There we go into more detail.
This volume is devoted to groups of Lie type and their geometries. The p-group complexes of a group G should be viewed as geometries for G. The p-group complexes of the groups of Lie type will be featured prominently here. In particular we will see that if G is of Lie type and characteristic p then the p-group complexes of G are homotopy equivalent to the building of G.
The term “simplicial complex” is used here to mean an abstract simplicial complex. Thus a simplicial complex K consists of a set K of objects called vertices together with a collection of finite subsets of K called simplices such that each subset of a simplex is a simplex.
- Type
- Chapter
- Information
- Groups of Lie Type and their Geometries , pp. 1 - 12Publisher: Cambridge University PressPrint publication year: 1995
- 1
- Cited by