Permutation Groups with a Cyclic Regular Subgroup and Arc Transitive Circulants

  title={Permutation Groups with a Cyclic Regular Subgroup and Arc Transitive Circulants},
  author={Caiheng Li},
  journal={Journal of Algebraic Combinatorics},
  • Caiheng Li
  • Published 1 March 2005
  • Mathematics
  • Journal of Algebraic Combinatorics
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 Kn, 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… 

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