Geometry of Sporadic Groups
Volume 2. Representations and Amalgams
Part of Encyclopedia of Mathematics and its Applications
- Authors:
- A. A. Ivanov, Imperial College of Science, Technology and Medicine, London
- S. V. Shpectorov, Bowling Green State University, Ohio
- Date Published: March 2002
- availability: Available
- format: Hardback
- isbn: 9780521623490
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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.
Read more- 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
See more reviews'… written with obvious care …'. EMS Newsletter
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×Product details
- Date Published: March 2002
- format: Hardback
- isbn: 9780521623490
- length: 304 pages
- dimensions: 235 x 159 x 22 mm
- weight: 0.56kg
- contains: 55 b/w illus. 15 tables
- availability: 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.
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