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arXiv · 2106.09676

On ECP-Groups

Viachaslau I. Murashka
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Abstract

According to T. Foguel a subgroup $H$ of a group $G$ is called conjugate-permutable if $ HH^x=H^xH$ for every $x\in G$. Mingyao Xu and Qinhai Zhang studied finite groups with every subgroup conjugate-permutable (ECP-groups) and asked three questions about them. We gave the answers on these questions. In particular, every group of exponent 3 is ECP-group, there exist non-regular ECP-$3$-groups and the class of all finite ECP-groups is neither formation nor variety.

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Viachaslau I. Murashka. 2021-06-17. On ECP-Groups. https://arxiv.org/abs/2106.09676

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