Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
MathSciNet review: 813805
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20F28, 20F24

Retrieve articles in all journals with MSC: 20F28, 20F24

Additional Information

Keywords: Automorphism group, torsion FC-group, semisimple group
Article copyright: © Copyright 1986 American Mathematical Society