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.