Conjugate-permutable subgroups (Q1357560)

A subgroup \(H\) of a group \(G\) is conjugate-permutable, if \(HH^g=H^gH\) for all elements \(g\in G\). The author obtains many properties of conjugate-permutable subgroups in finite and locally finite groups. For instance, he shows that every conjugate-permutable subgroup of a finite group is subnormal. He also gives examples of subnormal subgroups, which are not conjugate-permutable, and of conjugate-permutable subgroups, which are not quasinormal.