Geometry of Sporadic Groups: Volume 2, Representations and Amalgams

ISBN-13: 9780521623490 / Angielski / Twarda / 2002 / 304 str.

A. A. Ivanov; Sergei V. Shpectorov; S. V. Shpectorov

Opis

This second volume in a two-volume set provides a complete self-contained proof of the classification of geometries associated with sporadic simple groups: Petersen and tilde geometries. It 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. By way of their systematic treatment of group amalgams, the authors establish a deep and important mathematical result.

Recenzje

'… written with obvious care …'. EMS Newsletter

Spis treści

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.