Groups of Ree type in characteristic 3 acting on polytopes

Dimitri Leemans, Egon Schulte, Hendrik Van Maldeghem

Abstract


Every Ree group R(q), with q ≠ 3 an odd power of 3, is the automorphism group of an abstract regular polytope, and any such polytope is necessarily a regular polyhedron (a map on a surface). However, an almost simple group G with R(q) < G ≤ Aut(R(q)) is not a C-group and therefore not the automorphism group of an abstract regular polytope of any rank.


Keywords


Abstract regular polytopes, string C-groups, small Ree groups, permutation groups

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ISSN: 1855-3974

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