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Intransitive Geometries
Author(s) -
Gramlich Ralf,
van Maldeghem Hendrik
Publication year - 2006
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1017/s0024611506015851
Subject(s) - mathematics , lemma (botany) , transitive relation , connection (principal bundle) , automorphism , pure mathematics , class (philosophy) , simple (philosophy) , algebra over a field , combinatorics , geometry , computer science , artificial intelligence , ecology , philosophy , poaceae , epistemology , biology
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. 2000 Mathematics Subject Classification 20E06, 05E20, 05E25, 51A05.