%0 Journal Article
%T A note on fixed points of automorphisms of infinite groups
%J International Journal of Group Theory
%I University of Isfahan
%Z 2251-7650
%A de Giovanni, Francesco
%A Newell, Martin L.
%A Russo, Alessio
%D 2014
%\ 12/01/2014
%V 3
%N 4
%P 57-61
%! A note on fixed points of automorphisms of infinite groups
%K automorphism group
%K Schur's theorem
%K absolute centre
%R 10.22108/ijgt.2014.5342
%X 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.
%U https://ijgt.ui.ac.ir/article_5342_1e6c5c18b97f38824f43a2febfd71900.pdf