On finite A-perfect abelian groups

Abstract

‎Let $G$ be a group and $A=Aut(G)$ be the group of automorphisms of‎ ‎$G$‎. ‎Then the element $[g,alpha]=g^{-1}alpha(g)$ is an‎ ‎autocommutator of $gin G$ and $alphain A$‎. ‎Also‎, ‎the‎ ‎autocommutator subgroup of G is defined to be‎ ‎$K(G)=langle[g,alpha]|gin G‎, ‎alphain Arangle$‎, ‎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.