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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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 | References | Similar Articles | Additional Information

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?)

  • 1. D. Leemans and L. Vauthier.
    An atlas of abstract regular polytopes for small groups. Aequationes Math., to appear.
  • 2. P. McMullen and E. Schulte.
    Abstract regular polytopes, volume 92 of Encyclopedia of Mathematics and its Applications.
    Cambridge University Press, Cambridge, 2002. MR 1965665 (2004a:52020)
  • 3. M. Suzuki.
    On a class of doubly transitive groups.
    Ann. of Math., 75:105-145, 1962. MR 0136646 (25:112)

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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
PII: S 0002-9939(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.