Geometry of Sporadic Groups: Volume 2, Representations and Amalgams

The second in a two-volume set, for researchers into finite groups, geometry and algebraic combinatorics.

A. A. Ivanov (Author), S. V. Shpectorov (Author)

9780521623490, Cambridge University Press

Hardback, published 14 March 2002

304 pages, 55 b/w illus. 15 tables
23.5 x 15.9 x 2.2 cm, 0.56 kg

'… written with obvious care …'. EMS Newsletter

This is the second volume in a two-volume set, which provides a complete self-contained proof of the classification of geometries associated with sporadic simple groups: Petersen and tilde geometries. The second volume contains a study of the representations of the geometries under consideration in GF(2)-vector spaces as well as in some non-abelian groups. The central part is the classification of the amalgam of maximal parabolics, associated with a flag transitive action on a Petersen or tilde geometry. The classification is based on the method of group amalgam, the most promising tool in modern finite group theory. Via their systematic treatment of group amalgams, the authors establish a deep and important mathematical result. This book will be of great interest to researchers in finite group theory, finite geometries and algebraic combinatorics.

1. Preliminaries
Part I. Representations: 2. General features
3. Classical geometries
4. Mathieu groups and Held group
5. Conway groups
6. Involution geometries
7. Large sporadics
Part II. Amalgams: 8. Method of group amalgams
9. Action on the derived graph
10. Shapes of amalgams
11. Amalgams for P-geometries
12. Amalgams for T-geometries
Concluding remarks: 13. Further developments.

Subject Areas: Geometry [PBM], Algebra [PBF]