Rendiconti del Seminario Matematico della Università di Padova


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Volume 127, 2012, pp. 249–255
DOI: 10.4171/RSMUP/127-13

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

B.A.F. Wehrfritz[1]

(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 [1] 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