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.
Rezensionen / Stimmen
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 fuer Mathematik
Reihe
Sprache
Verlagsort
Zielgruppe
Illustrationen
25 Line drawings, unspecified
Maße
Höhe: 235 mm
Breite: 157 mm
Dicke: 29 mm
Gewicht
ISBN-13
978-0-521-41362-6 (9780521413626)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Autor*in
Imperial College of Science, Technology and Medicine, London
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.
