Geometry of Sporadic Groups

Volume 1, Petersen and Tilde Geometries
Erscheinungsjahr 2002
ISBN: 978-0-521-41362-6
Verlag: Cambridge University Press

Buch, Englisch, Band 76, 422 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 836 g

Reihe: Encyclopedia of Mathematics and its Applications

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.

Autoren/Hrsg.

Ivanov, A. A.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Geometrie
• Mathematik | Informatik Mathematik Operations Research Graphentheorie
• Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie

Inhaltsverzeichnis

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.