Finite groups with coprime fixed-point-free automorphisms and applications

Lei Wang; Yin Liu

Finite groups with coprime fixed-point-free automorphisms and applications

Group Theory 2018-01-30 v2

Authors: Lei Wang , Yin Liu

Abstract

We study a class of finite groups $G$ which behave similarly to elementary abelian $p$ -groups with $p$ prime, that is, there exists a subgroup $N$ such that all elements of $G\setminus N$ are conjugate or inverse-conjugate under $\Aut(G)$ . In this paper, we show that such groups are solvable. As an application, we characterise a class of normal edge-transitive Cayley graphs of $G$ , which are complete multipartite graphs.

Keywords

cayley graphs group theory graph theory of groups

Cite

@article{arxiv.1609.05635,
  title  = {Finite groups with coprime fixed-point-free automorphisms and applications},
  author = {Lei Wang and Yin Liu},
  journal= {arXiv preprint arXiv:1609.05635},
  year   = {2018}
}

Comments

There were some minor problems and the results changed

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