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;?] = g^-1 ?(g) is an autocommutator of g ? G and ? ? A. Also, the autocommutator subgroup of G is defined to be K(G) = [g;? ]|g ? G; ? ? A, 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.