On the Fixed-Point Set and Commutator Subgroup of an Authomorphism of a Group of Finite Rank

Abstract

Let $\varphi$ be an automorphism of a group $G$. For $G$ polycyclic, Endimioni and Moravec in [1] discuss the relationship between the fixed-point set $C_G(\varphi )$ and the commutator subgroup $[G,\varphi ]$ of $\varphi$ in $G$. Here we extend these results to soluble groups satisfying various rank restrictions.