A. A. Ivanov
Imperial College of Science, Technology and Medicine, London
By S. V. Shpectorov
Bowling Green State University, Ohio
Publisher: Cambridge University Press
Print Publication Year:2002
Online Publication Date:July 2010
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.