ALL ALTERNATING GROUPS A(n) WITH n %26gt;= 12 HAVE POLYTOPES OF RANK [n-1/2]

作者：Fernandes Maria Elisa^*; Leemans Dimitri; Mixer Mark

来源：SIAM Journal on Discrete Mathematics, 2012, 26(2): 482-498.

DOI：10.1137/110838467

• polytopes
• Coxeter groups
• alternating groups

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 %26gt;= 3, with automorphism group isomorphic to A(2r+3) when r is odd, and A(2r+1) when r is even. In this paper, the remaining cases are completed. It is shown that every group A(n), 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 %26gt;= 12.

• 出版日期2012