Geometry of Sporadic Groups
Geometry of Sporadic Groups
S. V. Shpectorov, Bowling Green State University, Ohio
£132.00
GBPThis 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.
- Complete proof of an important result in mathematics
- Self contained and with section on future developments for those pursuing research in this area
- The second in a two-volume set
Reviews & endorsements
'The book is written with obvious care and the arguments are usually not difficult to follow. The authors have also taken care with summaries and overviews that ease understanding of the general strategy of the proof.' European Mathematical Society
'… written with obvious care …'. EMS Newsletter
Product details
March 2002Hardback
9780521623490
304 pages
235 × 159 × 22 mm
0.56kg
55 b/w illus. 15 tables
Available
Table of Contents
- 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.
