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arXiv · 1606.02097

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
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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 $\mathrm{Alt}(5)$ or $\mathrm{Sym}(5)$.

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Joanna B. Fawcett, Michael Giudici, Cai Heng Li, Cheryl E. Praeger, Gordon Royle, Gabriel Verret. 2016-06-07. Primitive permutation groups with a suborbit of length 5 and vertex-primitive graphs of valency 5. https://doi.org/10.1016/j.jcta.2018.02.008

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