Abstract
A description is given of finite permutation groups containing a cyclic regular subgroup. It is then applied to derive a classification of arc transitive circulants, completing the work dating from 1970’s. It is shown that a connected arc transitive circulant Γ of order n is one of the following: a complete graph K n , a lexicographic product \(\Sigma [{\bar K}_b]\), a deleted lexicographic product \(\Sigma [{\bar K}_b] - b\Sigma\), where Σ is a smaller arc transitive circulant, or Γ is a normal circulant, that is, AutaΓ has a normal cyclic regular subgroup. The description of this class of permutation groups is also used to describe the class of rotary Cayley maps in subsequent work.
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1991 MR Subject Classification: 20B15, 20B30, 05C25
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Li, C.H. Permutation Groups with a Cyclic Regular Subgroup and Arc Transitive Circulants. J Algebr Comb 21, 131–136 (2005). https://doi.org/10.1007/s10801-005-6903-3
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DOI: https://doi.org/10.1007/s10801-005-6903-3