English

Characterising CCA Sylow cyclic groups whose order is not divisible by four

Combinatorics 2017-04-06 v2 Group Theory

Abstract

A Cayley graph on a group GG has a natural edge-colouring. We say that such a graph is CCA if every automorphism of the graph that preserves this edge-colouring is an element of the normaliser of the regular representation of GG. A group GG is then said to be CCA if every Cayley graph on GG is CCA. Our main result is a characterisation of non-CCA graphs on groups that are Sylow cyclic and whose order is not divisible by four. We also provide several new constructions of non-CCA graphs.

Keywords

Cite

@article{arxiv.1702.06651,
  title  = {Characterising CCA Sylow cyclic groups whose order is not divisible by four},
  author = {Luke Morgan and Joy Morris and Gabriel Verret},
  journal= {arXiv preprint arXiv:1702.06651},
  year   = {2017}
}

Comments

New version makes minor corrections to statements of Lemma 2.4 and Theorem 4.4

R2 v1 2026-06-22T18:24:51.465Z