On a problem on explicit embeddings of the group ℚ

An explicit embedding mentioned in this problem is possible and, moreover, the finitely generated group G can in fact be two-generator. This, of course, stresses the similarity of the constructed embedding with the embedding of [4] because the latter, too, is an embedding into a two-generator group. In the current paper, we suggest two mechanisms to build the embedding mentioned. The first argument uses the operation of wreath products, while the second argument is based on Higman-Neumann-Neumann extensions (HNN extensions) of groups. For general group-theoretical background information, we refer to [5, 15]. More specific information on wreath products can be found in [12], and on generalized free products and HNN extensions can be found in [6, 14]. For original methods and techniques of work with embeddings of countable groups in two-generator groups, we refer to wellknown articles [2, 3, 4, 11].