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Almost simple groups of Suzuki type acting on polytopes

Authors:	Dimitri Leemans

Institution:	Département de Mathématiques, Université Libre de Bruxelles, C.P.216 - Géométrie, Boulevard du Triomphe, 1050 Bruxelles, Belgium

Abstract:	Let , with $q\neq 2$ an odd power of two. For each almost simple group such that $S < G \leq Aut(S)$ , we prove that is not a C-group and therefore is not the automorphism group of an abstract regular polytope. For , we show that there is always at least one abstract regular polytope $\mathcal{P}$ such that $G = Aut(\mathcal{P})$ . Moreover, if $\mathcal{P}$ is an abstract regular polytope such that $G = Aut(\mathcal{P})$ , then $\mathcal{P}$ is a polyhedron.

Keywords:	String C-groups abstract regular polytopes thin regular geometries Suzuki simple groups

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