Torsion-free Abelian Factor Groups of the Baumslag-Solitar Groups and Subgroups of the Additive Group of the Rational Numbers

Abstract

The object of this paper is to give a proof of the following theorem: S/P ≅ Λ mn ⊆ ℚ+, where S/P is a certain torsion-free factor group of the Baumslag-Solitar group 〈a, b; a –1 bma = bn | m ≠ 0, n ≠ 0, m, n ∈ ℤ〉, with m and n are relatively prime, and Λ mn is a subgroup of the additive group of the rational numbers ℚ+.