Finite groups with only subnormal or self-normal subgroups (Q2704547)

A subgroup \(H\) of a finite group \(G\) is said to be abnormal if \(g\in\langle H,H^g\rangle\) for all \(g\in G\) and self-normal if \(N_G(H)=H\). In this paper, the authors give an explicit description of those finite groups for which every subgroup is either subnormal or self-normal. In particular, they prove that these groups are the same as those finite groups in which every subgroup is either subnormal or abnormal.