Geometry of Sporadic Groups

Erscheinungsjahr 2018
ISBN: 978-0-521-62349-0
Verlag: Cambridge University Press

Buch, Englisch, Band 91, 304 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 650 g

Reihe: Encyclopedia of Mathematics and its Applications

This is the second volume in a two-volume set, which provides a complete self-contained proof of the classification of geometries associated with sporadic simple groups: Petersen and tilde geometries. The second volume contains a study of the representations of the geometries under consideration in GF(2)-vector spaces as well as in some non-abelian groups. The central part is the classification of the amalgam of maximal parabolics, associated with a flag transitive action on a Petersen or tilde geometry. The classification is based on the method of group amalgam, the most promising tool in modern finite group theory. Via their systematic treatment of group amalgams, the authors establish a deep and important mathematical result. This book will be of great interest to researchers in finite group theory, finite geometries and algebraic combinatorics.

Autoren/Hrsg.

Ivanov, A. A

Shpectorov, S. V

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

1. Preliminaries; Part I. Representations: 2. General features; 3. Classical geometries; 4. Mathieu groups and Held group; 5. Conway groups; 6. Involution geometries; 7. Large sporadics; Part II. Amalgams: 8. Method of group amalgams; 9. Action on the derived graph; 10. Shapes of amalgams; 11. Amalgams for P-geometries; 12. Amalgams for T-geometries; Concluding remarks: 13. Further developments.