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
收藏
页码：1248 / 1257
页数：10
相关论文
共 50 条
  • [21] Regular maps with nilpotent automorphism group
    Conder, Marston
    Du, Shaofei
    Nedela, Roman
    Skoviera, Martin
    JOURNAL OF ALGEBRAIC COMBINATORICS, 2016, 44 (04) : 863 - 874
  • [22] Regular dessins with a given automorphism group
    Jones, Gareth A.
    RIEMANN AND KLEIN SURFACES, AUTOMORPHISMS, SYMMETRIES AND MODULI SPACES, 2014, 629 : 245 - 260
  • [23] Designs with a simple automorphism group ☆
    Montinaro, Alessandro
    Zhao, Yanwei
    Zhang, Zhilin
    Zhou, Shenglin
    FINITE FIELDS AND THEIR APPLICATIONS, 2024, 99
  • [24] The Diameter and Automorphism Group of Gelfand-Tsetlin Polytopes
    Gao, Yibo
    Krakoff, Benjamin
    Yang, Lisa
    DISCRETE & COMPUTATIONAL GEOMETRY, 2019, 62 (01) : 209 - 238
  • [25] Some enumerations of regular hypermaps with automorphism group isomorphic to PSL(2)(q).
    Downs, M
    QUARTERLY JOURNAL OF MATHEMATICS, 1997, 48 (189): : 39 - 58
  • [26] ON THE ZETA FUNCTION AND THE AUTOMORPHISM GROUP OF THE GENERALIZED SUZUKI CURVE
    Borges, Herivelto
    Coutinho, Mariana
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2021, 374 (03) : 1899 - 1917
  • [27] NUMBER OF GRAPHS WITH A GIVEN AUTOMORPHISM GROUP
    SHEEHAN, J
    CANADIAN JOURNAL OF MATHEMATICS, 1968, 20 (05): : 1068 - &
  • [28] On the automorphism group of a distance-regular graph
    Pyber, Laszlo
    Skresanov, Saveliy V.
    JOURNAL OF COMBINATORIAL THEORY SERIES B, 2025, 172 : 94 - 114
  • [29] SEMIGROUPS WHOSE REGULAR REPRESENTATION IS A GROUP
    CHRISLOCK, JL
    PROCEEDINGS OF THE JAPAN ACADEMY, 1964, 40 (10): : 799 - +
  • [30] A new algorithm to classify chiral polytopes with a given automorphism group
    Francis Buekenhout
    Dimitri Leemans
    Philippe Tranchida
    Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2021, 62 : 21 - 36
12345