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Almost simple groups of Suzuki type acting on polytopes


Author: Dimitri Leemans
Journal: Proc. Amer. Math. Soc. 134 (2006), 3649-3651
MSC (2000): Primary 52B11; Secondary 20D06
Published electronically: June 29, 2006
MathSciNet review: 2240679
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Abstract: Let $ S = Sz(q)$, with $ q\neq 2$ an odd power of two. For each almost simple group $ G$ such that $ S < G \leq Aut(S)$, we prove that $ G$ is not a C-group and therefore is not the automorphism group of an abstract regular polytope. For $ G = Sz(q)$, 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.


References [Enhancements On Off] (What's this?)

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    An atlas of abstract regular polytopes for small groups. Aequationes Math., to appear.
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  • 3. Michio Suzuki, On a class of doubly transitive groups, Ann. of Math. (2) 75 (1962), 105–145. MR 0136646

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Additional Information

Dimitri Leemans
Affiliation: Département de Mathématiques, Université Libre de Bruxelles, C.P.216 - Géométrie, Boulevard du Triomphe, 1050 Bruxelles, Belgium
Email: dleemans@ulb.ac.be

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08448-6
Keywords: String C-groups, abstract regular polytopes, thin regular geometries, Suzuki simple groups
Received by editor(s): June 24, 2005
Received by editor(s) in revised form: August 1, 2005
Published electronically: June 29, 2006
Communicated by: John R. Stembridge
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.