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arXiv · 1508.00717

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

Xingzheng Tang·Xiaoyu Chen·Wenbin Guo
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Abstract

Assume that a finite group $G$ admits a Frobenius group of automorphisms $FH$ 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.

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Xingzheng Tang, Xiaoyu Chen, Wenbin Guo. 2015-08-04. On supersolubility of finite groups admitting a Frobenius group of automorphisms with fixed-point-free kernel. https://arxiv.org/abs/1508.00717

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