On supersolubility of finite groups admitting a Frobenius group of automorphisms with fixed-point-free kernel

Xingzheng Tang; Xiaoyu Chen; Wenbin Guo

paper

On supersolubility of finite groups admitting a Frobenius group of automorphisms with fixed-point-free kernel

arXiv:1508.00717

Abstract

Assume that a finite group $G$ admits a Frobenius group of automorphisms $F H$ with kernel $F$ and complement $H$ such that $C_{G} (F) = 1$ . In this paper, we investigate this situation and prove that if $C_{G} (H)$ is supersoluble and $C_{G^{'}} (H)$ is nilpotent, then $G$ is supersoluble. Also, we show that $G$ is a Sylow tower group of a certain type if $C_{G} (H)$ is a Sylow tower group of the same type.