### 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).

Language | English |
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Pages | 247-266 |

Number of pages | 20 |

Journal | Journal of Combinatorial Theory. Series A |

Volume | 157 |

DOIs | |

Publication status | Published - 1 Jul 2018 |

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### Cite this

*Journal of Combinatorial Theory. Series A*,

*157*, 247-266. https://doi.org/10.1016/j.jcta.2018.02.008

}

*Journal of Combinatorial Theory. Series A*, vol. 157, pp. 247-266. https://doi.org/10.1016/j.jcta.2018.02.008

**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.

Research output: Contribution to journal › Article

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 -