English

On ECP-Groups

Group Theory 2021-06-18 v1

Abstract

According to T. Foguel a subgroup HH of a group GG is called conjugate-permutable if HHx=HxH HH^x=H^xH for every xGx\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-33-groups and the class of all finite ECP-groups is neither formation nor variety.

Keywords

Cite

@article{arxiv.2106.09676,
  title  = {On ECP-Groups},
  author = {Viachaslau I. Murashka},
  journal= {arXiv preprint arXiv:2106.09676},
  year   = {2021}
}
R2 v1 2026-06-24T03:19:40.759Z