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On a problem on explicit embeddings of the group \(\mathbb{Q}\). (English) Zbl 1095.20016
The author gives some explicit embeddings of the additive group of rational numbers \(\mathbb{Q}\) into a finitely generated group \(G\) (the group \(G\) in fact is two-generator, and the constructed embedding can be subnormal and preserves a few properties such as solubility or torsion freeness). The author suggests 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 of groups.

MSC:
20E22 Extensions, wreath products, and other compositions of groups
20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
20E07 Subgroup theorems; subgroup growth
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