The Structure of EAP-Groups and Self-Autopermutable Subgroups

Abstract EN

A subgroup H of a given group G is said to be autopermutable,if HHα=HαH for all α∈AutG.

We alsocall H a self-autopermutable subgroup of G, when HHα=HαH implies that Hα=H.

Moreover, G is said to be EAP-group, if every subgroup of G isautopermutable.

One notes that if α runs over the inner automorphisms of the group, one obtains the notions of conjugate-permutability, self-conjugate-permutability,and ECP-groups, which were studied by Foguel in 1997, Liand Meng in 2007, and Xu and Zhang in 2005, respectively.

In the present paper, we determine the structure of a finite EAP-group when its centre is of index 4 in G.

We also show that self-autopermutability and characteristic properties are equivalent for nilpotent groups.