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Centralizers in residually finite torsion groups

Author: Aner Shalev
Journal: Proc. Amer. Math. Soc. 126 (1998), 3495-3499
MSC (1991): Primary 20F50, 20E36; Secondary 20F40, 17B01
MathSciNet review: 1459149
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Abstract: Let $G$ be a residually finite torsion group. We show that, if $G$ has a finite 2-subgroup whose centralizer is finite, then $G$ is locally finite. We also show that, if $G$ has no $2$-torsion, and $Q$ is a finite 2-group acting on $G$ in such a way that the centralizer $C_G(Q)$ is soluble, or of finite exponent, then $G$ is locally finite.

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Additional Information

Aner Shalev
Affiliation: Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel

Received by editor(s): March 25, 1997
Received by editor(s) in revised form: April 23, 1997
Additional Notes: Supported by the Bi-National Science Foundation United States – Israel, Grant No. 92-00034
Dedicated: In memory of Brian Hartley
Communicated by: Lance W. Small
Article copyright: © Copyright 1998 American Mathematical Society

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