Digraph Representations of 2-closed Permutation Groups with a Normal Regular Cyclic Subgroup

Jing Xu

Abstract


In this paper, we classify 2-closed (in Wielandt's sense) permutation groups which contain a normal  regular cyclic subgroup and prove that for each such group $G$, there exists a circulant $\Gamma$ such that $\mathrm{Aut} (\Gamma)=G$.


Keywords


2-closed permutation groups, Digraph representations, Arc-transitive circulants

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