Petersen and tilde geometries
著者
書誌事項
Petersen and tilde geometries
（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, 76 . Geometry of sporadic groups ; 1）
Cambridge University Press, 2008 c1999
- : pbk
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注記
Bibliography: p. 398-405
Includes index
"Paperback re-issue"--Cover
"This digitally version 2008"--T.p. verso
内容説明・目次
内容説明
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.
目次
- 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.
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