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

Research output: Contribution to journalArticle

  • 1 Citations

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).

LanguageEnglish
Pages247-266
Number of pages20
JournalJournal of Combinatorial Theory. Series A
Volume157
DOIs
StatePublished - 1 Jul 2018

Fingerprint

Primitive Group
Permutation group
Graph in graph theory
Vertex of a graph
Classify
Maximal Subgroup
Simple group
Corollary
Isomorphic

Cite this

@article{68fc36f3b85f4eed8812ca170d0c0938,
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",
month = "7",
day = "1",
doi = "10.1016/j.jcta.2018.02.008",
language = "English",
volume = "157",
pages = "247--266",
journal = "Journal of Combinatorial Theory Series A",
issn = "0021-9800",
publisher = "Academic Press",

}

Primitive permutation groups with a suborbit of length 5 and vertex-primitive graphs of valency 5. / Fawcett, Joanna B.; Giudici, Michael; Li, Cai Heng; Praeger, Cheryl E.; Royle, Gordon; Verret, Gabriel.

In: Journal of Combinatorial Theory. Series A, Vol. 157, 01.07.2018, p. 247-266.

Research output: Contribution to journalArticle

TY - JOUR

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 - http://www.scopus.com/inward/record.url?scp=85042643370&partnerID=8YFLogxK

U2 - 10.1016/j.jcta.2018.02.008

DO - 10.1016/j.jcta.2018.02.008

M3 - Article

VL - 157

SP - 247

EP - 266

JO - Journal of Combinatorial Theory Series A

T2 - Journal of Combinatorial Theory Series A

JF - Journal of Combinatorial Theory Series A

SN - 0021-9800

ER -