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ON LOCAL FINITENESS OF PERIODIC RESIDUALLY FINITE GROUPS

Published online by Cambridge University Press:  14 October 2002

Mahmut Kuzucuoğlu  and
Pavel Shumyatsky
Mahmut Kuzucuoğlu
Affiliation:
Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey (matmah@metu.edu.tr)
Pavel Shumyatsky
Affiliation:
Department of Mathematics, University of Brasilia, Brasilia-DF, Brazil (pavel@ipe.mat.unb.br)
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Abstract

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Let $G$ be a periodic residually finite group containing a nilpotent subgroup $A$ such that $C_G(A)$ is finite. We show that if $\langle A,A^g\rangle$ is finite for any $g\in G$, then $G$ is locally finite.

AMS 2000 Mathematics subject classification: Primary 20F50

Keywords

automorphismscentralizersperiodic groups
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 45 , Issue 3 , October 2002 , pp. 717 - 721
Copyright
Copyright © Edinburgh Mathematical Society 2002