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International Journal of Mathematics and Mathematical Sciences
Volume 2005, Issue 14, Pages 2287-2298
http://dx.doi.org/10.1155/IJMMS.2005.2287

Abelian subgroup separability of some one-relator groups

Department of Mathematics and Computer Science, University of Ngaoundere, P.O. Box 454, Ngaoundere, Cameroon

Received 29 August 2004; Revised 11 June 2005

Copyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We prove that any group in the class of one-relator groups given by the presentation a,b;[am,bn]=1, where m and n are integers greater than 1, is cyclic subgroup separable (or πc). We establish some suitable properties of these groups which enable us to prove that every finitely generated abelian subgroup of any of such groups is finitely separable.