On finite A-perfect abelian groups - Mohammad Mehdi Nasrabadi; Ali Gholamian (International Journal of Group Theory, 2012)
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 $K(G) =< [g,alpha] gin G, alphain A >$, which is a characteristic subgroup of G containing the derived sub- group $G'$ 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.