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...
Main Authors: | , , |
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Format: | Article |
Language: | English |
Published: |
University of Isfahan
2014-12-01
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Series: | International Journal of Group Theory |
Subjects: | |
Online Access: | http://www.theoryofgroups.ir/pdf_5342_1e6c5c18b97f38824f43a2febfd71900.html |
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. |
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ISSN: | 2251-7650 2251-7669 |