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.
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de Giovanni, F. , Newell, M. L. and Russo, A. (2014). A note on fixed points of automorphisms of infinite groups. International Journal of Group Theory, 3(4), 57-61. doi: 10.22108/ijgt.2014.5342
MLA
de Giovanni, F. , , Newell, M. L. , and Russo, A. . "A note on fixed points of automorphisms of infinite groups", International Journal of Group Theory, 3, 4, 2014, 57-61. doi: 10.22108/ijgt.2014.5342
HARVARD
de Giovanni, F., Newell, M. L., Russo, A. (2014). 'A note on fixed points of automorphisms of infinite groups', International Journal of Group Theory, 3(4), pp. 57-61. doi: 10.22108/ijgt.2014.5342
CHICAGO
F. de Giovanni , M. L. Newell and A. Russo, "A note on fixed points of automorphisms of infinite groups," International Journal of Group Theory, 3 4 (2014): 57-61, doi: 10.22108/ijgt.2014.5342
VANCOUVER
de Giovanni, F., Newell, M. L., Russo, A. A note on fixed points of automorphisms of infinite groups. International Journal of Group Theory, 2014; 3(4): 57-61. doi: 10.22108/ijgt.2014.5342