A note on fixed points of automorphisms of infinite groups

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, provide...

Full description

Bibliographic Details
Main Authors: Francesco de Giovanni, Martin L. Newell, Alessio Russo
Format: Article
Language:English
Published: University of Isfahan 2014-12-01
Series:International Journal of Group Theory
Subjects:
Online Access:http://www.theoryofgroups.ir/pdf_5342_1e6c5c18b97f38824f43a2febfd71900.html
Description
Summary: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.
ISSN:2251-7650
2251-7669