Document Type : Original Manuscript


Department of Mathematical Sciences, Isfahan University of Technology, P. O. Box 84156-83111, Isfahan, Iran.



‎Suppose that $G$ is a finite group. ‎The acentralizer $C_G(\alpha)$ of an automorphism $\alpha$ of $G$‎,
‎is defined as the subgroup of fixed points of $\alpha$‎, ‎that is $C_G(\alpha)= \{g \in G \mid \alpha(g)=g\}$‎.
‎In this paper we determine the acentralizers of groups of order $p^3$‎, ‎where $p$ is a prime number.


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