On finite A-perfect abelian groups

‎Let G be a group and A=Aut(G) be the group of automorphisms of‎ ‎G‎. ‎Then the element [g,\alpha]=g^{-۱}\alpha(g) is an‎ ‎autocommutator of g\in G and \alpha\in A‎. ‎Also‎, ‎the‎ ‎autocommutator subgroup of G is defined to be‎ ‎K(G)=\langle[g,\alpha]|g\in G‎, ‎\alpha\in A\rangle‎, ‎which is a‎ ‎characteristic subgroup of G containing the derived subgroup‎ ‎G' of G‎. ‎A group is defined as A-perfect‎, ‎if it equals its own‎ ‎autocommutator subgroup‎. ‎The present research is aimed at‎ ‎classifying finite abelian groups which are A-perfect‎.

Keywords:

Automorphism , Autocommutator subgroup , A-perfect group , Finite abelian group