Abelian groups as autocommutator subgroups

摘要

In this paper, we discuss special abelian subgroups of autocommutator group of a finite abelian group. Indeed, for a finite abelian group A, we determine when the equations [X, Inv(Aut(X))]≌ A, [X, Aut(X)']≌ A and [X, Aut(X)~2]≌ A are solvable on finite abelian groups.