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Polytopes of high rank for the alternating groups

par Fernandes, Maria Elisa;Leemans, Dimitri ;Mixer, Mark
Référence Journal of combinatorial theory. Series A, 119, 1, page (42-56)
Publication Publié, 2012

Article révisé par les pairs

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Résumé :

There is a well-known correspondence between abstract regular polytopes and string C-groups. In this paper, for each d≥. 3, a string C-group with d generators, isomorphic to an alternating group of degree n is constructed (for some n≥. 9), or equivalently an abstract regular d-polytope, is produced with automorphism group Alt(n). A method that extends the CPR graph of a polytope to a different CPR graph of a larger (or possibly isomorphic) polytope is used to prove that various groups are themselves string C-groups. © 2011 Elsevier Inc.