University of Isfahan International Journal of Group Theory 2251-7650 3 4 2014 12 01 A note on fixed points of automorphisms of infinite groups 57 61 5342 10.22108/ijgt.2014.5342 EN Francesco De Giovanni University of Napoli Federico II Martin L. Newell National University of Ireland Alessio Russo Seconda Universita di Napoli Journal Article 2014 04 15 ‎Motivated by a celebrated theorem of Schur‎, ‎we show that if $\Gamma$ is a normal subgroup of the full automorphism group $Aut(G)$ of a group $G$ such that $Inn(G)$ is contained in $\Gamma$ and $Aut(G)/\Gamma$ has no uncountable abelian subgroups of prime exponent‎, ‎then $[G,\Gamma]$ is finite‎, ‎provided that the subgroup consisting of all elements of $G$ fixed by $\Gamma$ has finite index‎. ‎Some applications of this result are also given.‎ https://ijgt.ui.ac.ir/article_5342_1e6c5c18b97f38824f43a2febfd71900.pdf