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

Joanna B. Fawcett; Michael Giudici; Cai Heng Li; Cheryl E. Praeger; Gordon Royle; Gabriel Verret

doi:10.1016/j.jcta.2018.02.008

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

Joanna B. Fawcett
, Michael Giudici
, Cai Heng Li
, Cheryl E. Praeger
, Gordon Royle
, Gabriel Verret

School of Physics, Mathematics and Computing

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

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).

Original language	English
Pages (from-to)	247-266
Number of pages	20
Journal	Journal of Combinatorial Theory. Series A
Volume	157
DOIs	https://doi.org/10.1016/j.jcta.2018.02.008
Publication status	Published - 1 Jul 2018

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title = "Primitive permutation groups with a suborbit of length 5 and vertex-primitive graphs of valency 5",

abstract = "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).",

keywords = "Almost simple groups, Arc-transitive graph, Maximal subgroups, Primitive group, Valency five, Vertex-primitive graph",

author = "Fawcett, \{Joanna B.\} and Michael Giudici and Li, \{Cai Heng\} and Praeger, \{Cheryl E.\} and Gordon Royle and Gabriel Verret",

year = "2018",

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doi = "10.1016/j.jcta.2018.02.008",

language = "English",

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pages = "247--266",

journal = "Journal of Combinatorial Theory. Series A",

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T1 - Primitive permutation groups with a suborbit of length 5 and vertex-primitive graphs of valency 5

AU - Fawcett, Joanna B.

AU - Giudici, Michael

AU - Li, Cai Heng

AU - Praeger, Cheryl E.

AU - Royle, Gordon

AU - Verret, Gabriel

PY - 2018/7/1

Y1 - 2018/7/1

N2 - 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).

AB - 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).

KW - Almost simple groups

KW - Arc-transitive graph

KW - Maximal subgroups

KW - Primitive group

KW - Valency five

KW - Vertex-primitive graph

UR - https://www.scopus.com/pages/publications/85042643370

U2 - 10.1016/j.jcta.2018.02.008

DO - 10.1016/j.jcta.2018.02.008

M3 - Article

AN - SCOPUS:85042643370

SN - 0097-3165

VL - 157

SP - 247

EP - 266

JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

ER -

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

Abstract

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