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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:
 2e+23 Extensions, wreath products, and other compositions of groups 2e+07 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations 2e+08 Subgroup theorems; subgroup growth
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