TY - JOUR
ID - 5342
TI - A note on fixed points of automorphisms of infinite groups
JO - International Journal of Group Theory
JA - IJGT
LA - en
SN - 2251-7650
AU - de Giovanni, Francesco
AU - Newell, Martin L.
AU - Russo, Alessio
AD - University of Napoli Federico II
AD - National University of Ireland
AD - Seconda Universita di Napoli
Y1 - 2014
PY - 2014
VL - 3
IS - 4
SP - 57
EP - 61
KW - automorphism group
KW - Schur's theorem
KW - absolute centre
DO - 10.22108/ijgt.2014.5342
N2 - 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.
UR - https://ijgt.ui.ac.ir/article_5342.html
L1 - https://ijgt.ui.ac.ir/article_5342_1e6c5c18b97f38824f43a2febfd71900.pdf
ER -