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

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Cambridge University Press, Jun 17, 1999 - Mathematics - 424 pages
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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 nonsplit 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 that 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 identification of Y-groups is given. This is an essential purchase for researchers in finite group theory, finite geometries and algebraic combinatorics.
  

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Contents

Mathieu groups
49
Geometry of Mathieu groups
100
Conway groups
141
The Monster
210
From C to Tgeometries
272
Ygroups
332
Locally projective graphs
358
Bibliography
398
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Page 398 - NL Biggs, Designs, factors and codes in graphs, Quart. J. Math. Oxford (2), 26 (1975), 113-119.

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About the author (1999)

A. A. Ivanov is a Professor in the Mathematical Department at Imperial College, London and the Institute of System Analysis at the Russian Academy of Sciences, Moscow.