Rendiconti del Seminario Matematico della Università di Padova
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On the Fixed-Point Set and Commutator Subgroup of an Authomorphism of a Group of Finite RankB.A.F. Wehrfritz (1) Department of Mathematical Sciences, Queen Mary University of London, Mile End Road, E1 4NS, London, UK
Let $\phi$ be an automorphism of a group $G$. For $G$ polycyclic, Endimioni and Moravec in  discuss the relationship between the fixed-point set $C_G(\phi)$ and the commutator subgroup $[G,\phi]$ of $\phi$ in $G$. Here we extend these results to soluble groups satisfying various rank restrictions.
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Wehrfritz B.A.F.: On the Fixed-Point Set and Commutator Subgroup of an Authomorphism of a Group of Finite Rank. Rend. Sem. Mat. Univ. Padova 127 (2012), 249-255. doi: 10.4171/RSMUP/127-13