Abelian subgroup separability of some one-relator groups

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.