On the number of abstract regular polytopes whose automorphism group is a Suzuki simple group Sz(q)

被引：9

作者：

Kiefer, Ann ^{[1
]}

Leemans, Dimitri ^{[1
]}

机构：

[1] Univ Libre Bruxelles, Dept Math, B-1050 Brussels, Belgium

来源：

JOURNAL OF COMBINATORIAL THEORY SERIES A | 2010年 / 117卷 / 08期

关键词：

Abstract regular polytopes; String C-groups; Suzuki simple groups; Mobius inversion;

D O I：

10.1016/j.jcta.2010.01.001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We determine, up to isomorphism and duality, the number of abstract regular polytopes of rank three whose automorphism group is a Suzuki simple group Sz(q), with q an odd power of 2. No polytope of higher rank exists and, therefore, the formula obtained counts all abstract regular polytopes of Sz(q). Moreover, there are no degenerate polyhedra. We also obtain, up to isomorphism, the number of pairs of involutions. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：1248 / 1257

页数：10

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