Published in the United States of America by Cambridge University Press, New York www.cambridge.org

This digitally printed version 2008

A catalogue record for this publication is available from the British Library

Library of Congress Cataloguing in Publication data

Ivanov, A. A. Geometry of sporadic groups 1, Petersen and tilde geometries / A.A. Ivanov. p. cm.

Paperback Re-issue

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, closef related to each other: Petersen and tilde geometries. There is an infinite family ot tilde geometries associated with non-split extensions of symplectic groups over a field of 2 elements. Besides that there are 12 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 identification of Y-groups is given.
This is an essential purchase for researchers into finite group theory, finite geometries and algebraic combinatorics.