A note on fixed points of automorphisms of infinite groups
نویسندگان
1 University of Napoli Federico II
2 National University of Ireland
3 Seconda Universita di Napoli
doi
10.22108/ijgt.2014.5342چکیده
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.
