Primitive permutation groups with a suborbit of length 5 and vertex-primitive graphs of valency 5

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:157

Article

Fawcett, Joanna B.^1,3  Giudici, Michael¹  Li, Cai Heng²  Praeger, Cheryl E.¹  Royle, Gordon¹  Verret, Gabriel^1,4,5 

[1] Univ Western Australia, Ctr Math Symmetry & Computat, 35 Stirling Highway, Crawley, WA 6009, Australia

[2] South Univ Sci & Technol, Dept Math, Shenzhen 518055, Guangdong, Peoples R China

[3] Imperial Coll London, Dept Math, South Kensington Campus, London SW7 2AZ, England

[4] Univ Primorska, FAMNIT, Glagoljaska 8, SI-6000 Koper, Slovenia

[5] Univ Auckland, Dept Math, Private Bag 92019, Auckland 1142, New Zealand

关键词: Primitive group;    Vertex-primitive graph;    Arc-transitive graph;    Valency five;    Almost simple groups;    Maximal subgroups;   

DOI  :  10.1016/j.jcta.2018.02.008

来源: Elsevier

【 摘 要 】

We classify finite primitive permutation groups having a suborbit of length 5. As a corollary, we obtain a classification of finite vertex-primitive graphs of valency 5. In the process, we also classify finite almost simple groups that have a maximal subgroup isomorphic to Alt(5) or Sym(5). (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free