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2013 On the fixed-point set of an automorphism of a group
B. A. F. Wehrfritz
Publ. Mat. 57(1): 139-153 (2013).

Abstract

Let $\phi$ be an automorphism of a group $G$. Under various finiteness or solubility hypotheses, for example under polycyclicity, the commutator subgroup $[G, \phi]$ has finite index in $G$ if the fixed-point set $C_{G}(\phi)$ of $\phi$ in $G$ is finite, but not conversely, even for polycyclic groups $G$. Here we consider a stronger, yet natural, notion of what it means for $[G, \phi]$ to have 'finite index' in $G$ and show that in many situations, including $G$ polycyclic, it is equivalent to $C_{G}(\phi)$ being finite.

Citation

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B. A. F. Wehrfritz. "On the fixed-point set of an automorphism of a group." Publ. Mat. 57 (1) 139 - 153, 2013.

Information

Published: 2013
First available in Project Euclid: 18 December 2012

zbMATH: 1291.20029
MathSciNet: MR3058931

Subjects:
Primary: 20E36, 20F16

Rights: Copyright © 2013 Universitat Autònoma de Barcelona, Departament de Matemàtiques

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Vol.57 • No. 1 • 2013
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