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INTRANSITIVE GEOMETRIES

Published online by Cambridge University Press:  13 October 2006

RALF GRAMLICH  and
HENDRIK VAN MALDEGHEM
RALF GRAMLICH
Affiliation:
FB Mathematik/AG 5, TU Darmstadt, Schloßgartenstraße 7, 64289 Darmstadt, [email protected]
HENDRIK VAN MALDEGHEM
Affiliation:
Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281, S22, 9000 Gent, [email protected]
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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.

Keywords

20E0605E2005E2551A05
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 93 , Issue 3 , November 2006 , pp. 666 - 692
Copyright
2006 London Mathematical Society

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