A problem from the kourovka notebook on embeddings of the group mathbb{Q}

Answering the question of de la Harpe and Bridson in the Kourovka Notebook, Problem 14.10(b), we construct explicit embeddings of the additive group of rational numbers $ mathbb{Q} $ in a finitely generated group G. In fact, the group G is 2-generator, and the constructed embedding can be subnormal and preserve a few properties such as solubility or torsion freeness.