@article{article_546988, title={Acentralizers of Abelian groups of rank 2}, journal={Hacettepe Journal of Mathematics and Statistics}, volume={49}, pages={273–281}, year={2020}, DOI={10.15672/hujms.546988}, author={Mozafar, Zahar and Taeri, Bijan}, keywords={Automorphism,centralizer,Acentralizer,finite groups}, abstract={Let $G$ be a group. The Acentralizer of an automorphism $\alpha$ of $G$, is the subgroup of fixed points of $\alpha$, i.e.,  $C_G(\alpha)= \{g\in G \mid \alpha(g)=g\}$. We show that if $G$ is a  finite  Abelian  $p$-group of rank $2$, where $p$ is an odd prime, then the number of Acentralizers of $G$ is exactly the number of subgroups of $G$. More precisely, we show that for each  subgroup $U$ of $G$, there exists an automorphism $\alpha$ of $G$ such that $C_G(\alpha)=U$. Also we find the Acentralizers of infinite two-generator Abelian groups.}, number={1}, publisher={Hacettepe University}