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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Some properties of FC-groups which occur as automorphism groups


Author: Jay Zimmerman
Journal: Proc. Amer. Math. Soc. 96 (1986), 39-40
MSC: Primary 20F28; Secondary 20F24
DOI: https://doi.org/10.1090/S0002-9939-1986-0813805-2
MathSciNet review: 813805
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Abstract: We prove that if $ G$ is a group such that Aut $ G$ is a countably infinite torsion $ FC$-group, then Aut $ G$ contains an infinite locally soluble, normal subgroup and hence a nontrivial abelian normal subgroup. It follows that a countably infinite subdirect product of nontrivial finite groups, of which only finitely many have nontrivial abelian normal subgroups, is not the automorphism group of any group.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0813805-2
Keywords: Automorphism group, torsion FC-group, semisimple group
Article copyright: © Copyright 1986 American Mathematical Society