International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 14, Pages 2287-2298
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 D. Tieudjo. 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.
We prove that any group in the class of one-relator groups given
by the presentation , where
and are integers greater than 1, is cyclic subgroup separable
(or ). 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.