On finite A-perfect abelian groups

International Journal of Group Theory

关键词: Automorphism;    Autocommutator subgroup;    A-perfect group;    Finite abelian group;   

DOI  :  

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown