On a problem on explicit embeddings of the group ℚ

Abstract

Answering a question of de la Harpe and Bridson in the Kourovka Notebook, we build the explicit embeddings of the additive group of rational numbers ℚ in a finitely generated group G. The group G in fact is two-generator, and the constructed embedding can be subnormal and preserve a few properties such as solubility or torsion freeness.