Proceedings of the London Mathematical Society

Table of Contents - 2006 - Volume 93, Issue 03  


INTRANSITIVE GEOMETRIES

RALF GRAMLICH a1 and HENDRIK VAN MALDEGHEM a2
a1 FB Mathematik/AG 5, TU Darmstadt, Schloßgartenstraße 7, 64289 Darmstadt, Germany gramlich@mathematik.tu-darmstadt.de
a2 Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281, S22, 9000 Gent, Belgium hvm@cage.ugent.be

Article author query
gramlich r   [Google Scholar] 
van maldeghem h   [Google Scholar] 
 

Abstract

A lemma of Tits establishes a connection between the simple connectivity of an incidence geometry and the universal completion of an amalgam induced by a sufficiently transitive group of automorphisms of that geometry. In the present paper, we generalize this lemma to intransitive geometries, thus opening the door for numerous applications. We treat ourselves some amalgams related to intransitive actions of finite orthogonal groups, as a first class of examples.

(Published Online October 13 2006)
(Received October 20 2004)
(Revised November 9 2005)

Maths Classification

20E06; 05E20; 05E25; 51A05.