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All alternating groups an with N ≥ 12 have polytopes of rank [n-1/2]

par Fernandes, Maria Elisa;Leemans, Dimitri ;Mixer, Mark
Référence SIAM journal on discrete mathematics, 26, 2, page (482-498)
Publication Publié, 2012

Article révisé par les pairs

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Résumé :

Using the correspondence between abstract regular polytopes and string C-groups, in a recent paper [M. E. Fernandes, D. Leemans, and M. Mixer, J. Combin. Theory Ser. A, 119 (2012), pp. 42-56], we constructed an abstract regular polytope of rank r, for each r ≥ 3, with automorphism group isomorphic to A2r+3 when r is odd, and A2r+1 when r is even. In this paper, the remaining cases are completed. It is shown that every group An, with n sufficiently large, acts on at least one abstract regular polytope of rank [n-1/2]. We conjecture that this is the highest possible rank for n ≥ 12. © 2012 Society for Industrial and Applied Mathematics.