Abstract:
Given a homomorphically closed root class $\mathscr K$ of groups, we find a criterion for a Baumslag–Solitar group to be a residually $\mathscr K$-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.
Keywords:root class residuality, residual solubility, residual $\pi$-finiteness, Baumslag–Solitar groups, HNN-extension.
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