The root class residuality of Baumslag-Solitar groups

摘要

Given a homomorphically closed root class K of groups, we find a criterion for a Baumslag-Solitar group to be a residually K-group. In particular, we establish that all Baumslag-Solitar groups are residually soluble and a Baumslag-Solitar group is residually finite soluble if and only if it is residually finite.