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Groups Acting Transitively on Locally Finite Classical Tits Chamber Systems
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Published:June 1990
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Abstract
Tits chamber systems admitting a transitive group of automorphisms have seen considerable interest in the last six or seven years. As a general reference I want to mention the surveys (lectures held at the Como conference in 1984) by Kantor ([61) and Timmesfeld ([28]). Some notions have been developed, some methods such as the “amalgam method” have proved to be very powerful instruments since then; different notions used, however, cause people to use different sets of hypotheses, and sometimes the interested reader might have trouble to see how the numerous papers written fit together and whether the results achieved give a completeclassification of the objects one is interested in.The purpose of this survey is to state the classification theorem that has been achieved since Como, to give the list of “types” allowed by the theorem together with explicit examples found by many authors, finally describe the systems of subgroups used in the literature with their various relationships. Thereby, I will have to repeat parts of Timmesfeld’s survey, but will do so in order to be as clear as possible.
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