title: The structure of EAP-groups and self-autopermutable subgroups.
abstract: A subgroup H of a given group G is said to be autopermutable, if HH(α) = H(α)H for all α ∈ Aut(G). We also call H a self-autopermutable subgroup of G, when HH(α) = H(α)H implies that H(α) = H. Moreover, G is said to be EAP-group, if every subgroup of G is autopermutable. 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, Li and 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.
authors.affiliation: Department of Mathematics, Islamic Azad University, Mashhad Branch, Mashhad 9187147578, Iran.
authors.forename: Shima
authors.identifier: 0000-0003-4028-774X
authors.initials: S
authors.lastname: Housieni
authors.affiliation: Department of Mathematics, Islamic Azad University, Mashhad Branch, Mashhad 9187147578, Iran ; Department of Mathematics, Khayyam University, Mashhad 9189747178, Iran ; Centre of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, P.O. Box 1159-91775, Iran.
authors.forename: Mohammad Reza Rajabzadeh
authors.identifier: 0000-0003-2979-2390
authors.initials: MR
authors.lastname: Moghaddam
mesh_terms: D008962:Models, Theoretical; D011336:Probability