%0 Journal Article
%T On finite A-perfect abelian groups
%A Mohammad Mehdi Nasrabadi
%A Ali Gholamian
%J International Journal of Group Theory
%D 2012
%I University of Isfahan
%X 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.
%K Automorphism
%K Autocommutator subgroup
%K A-perfect group
%K Finite abelian group
%U http://www.theoryofgroups.ir/?_action=showPDF&article=764&_ob=c0e46ef10fc8cc8252147940e51d0023&fileName=full_text.pdf