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Acta Mathematica Vietnamica

ON THE FIXED-POINT SET AND COMMUTATOR SUBGROUP OF AN AUTOMORPHISM OF A SOLUBLE GROUP

B. A. F. WEHRFRITZ

Abstract

Let $\Phi$ be an automorphism of finite order of a group $G$. We deduce consequences for the commutator subgroup $[G, \Phi]$ of $\Phi$ on $G$ of hypotheses such as finiteness and local finiteness on the fixed-point set $C_G(\Phi)$ of $\Phi$ on $G$. We require various solubility or finiteness conditions on $G$ or at least on $[G, \Phi]$.