Permutation Groups with a Cyclic Regular Subgroup and Arc Transitive Circulants

  • Authors:

  • Cai Heng Li

  • Affiliations:

  • Aff1 Aff2

  • Venue:
  • Journal of Algebraic Combinatorics: An International Journal
  • Year:
  • 2005

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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 驴 of order n is one of the following: a complete graph Kn, a lexicographic product $\Sigma [{\bar K}_b]$ , a deleted lexicographic product $\Sigma [{\bar K}_b] - b\Sigma$ , where 驴 is a smaller arc transitive circulant, or 驴 is a normal circulant, that is, Auta驴 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.