Geometry of Sporadic Groups: Volume 1, Petersen and Tilde Geometries

Important monograph on finite group theory.

A. A. Ivanov (Author)

9780521062831, Cambridge University Press

Paperback / softback, published 15 May 2008

424 pages, 25 b/w illus.
22.9 x 15.3 x 2.4 cm, 0.642 kg

Review of the hardback: '… this book is an essential purchase for researcher in finite group theory, finite geometries and algebraic combinatorics.' Anatoli Kondrat'ev, Zentralblatt für Mathematik

This book is the first volume in a two-volume set, which will provide the complete proof of classification of two important classes of geometries, closely related to each other: Petersen and tilde geometries. There is an infinite family of tilde geometries associated with non-split extensions of symplectic groups over a field of two elements. Besides that there are twelve exceptional Petersen and tilde geometries. These exceptional geometries are related to sporadic simple groups, including the famous Monster group and this volume gives a construction for each of the Petersen and tilde geometries which provides an independent existence proof for the corresponding automorphism group. Important applications of Petersen and Tilde geometries are considered, including the so-called Y-presentations for the Monster and related groups, and a complete indentification of Y-groups is given. This is an essential purchase for researchers into finite group theory, finite geometries and algebraic combinatorics.

Preface
1. Introduction
2. Mathieu groups
3. Geometry of Mathieu groups
4. Conway groups
5. The monster
6. From Cn- to Tn-geometries
7. 2-covers of P-geometries
8. Y-groups
9. Locally projective graphs
Bibliography
Index.

Subject Areas: Combinatorics & graph theory [PBV], Topology [PBP], Geometry [PBM], Groups & group theory [PBG]