University of IsfahanInternational Journal of Group Theory2251-76503420141201A note on fixed points of automorphisms of infinite groups5761534210.22108/ijgt.2014.5342ENFrancescoDe GiovanniUniversity of Napoli Federico IIMartin L.NewellNational University of IrelandAlessioRussoSeconda Universita di Napoli0000-0002-5336-0347Journal Article20140415Motivated 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