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

DOI:
https://doi.org/10.1090/S0002-9939-98-04471-2

MathSciNet review:
1459149

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a residually finite torsion group. We show that, if has a finite 2-subgroup whose centralizer is finite, then is locally finite. We also show that, if has no -torsion, and is a finite 2-group acting on in such a way that the centralizer is soluble, or of finite exponent, then is locally finite.

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Additional Information

**Aner Shalev**

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

DOI:
https://doi.org/10.1090/S0002-9939-98-04471-2

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