Symmetry groups of vertex-transitive polytopes |
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Authors: | László Babai |
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Affiliation: | 1. Dept. of Algebra, E?tv?s L. University, Muzeum krt. 6-8, H-1088, Budapest, Hungary
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Abstract: | Groups which are not isomorphic to the symmetry group of any vertextransitive polytope (of any dimension) are characterized as generalized dicyclic, or abelian groups but not elementary 2-groups. The same class of groupsG is also characterized by the existence of a permutation groupP acting onG, containingG* (the regular representation ofG) as a proper subgroup, such that the members of the stabilizerP u of the unitu ε G take everyg ε G tog ±1. |
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