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Explicit embeddings of the group $\mathbb{Q}$ into a finitely presented group$\mathcal{Q}$ and into a $2$-generator finitely presented group$T_{\mathcal{Q}}$ are suggested. The constructed embeddings reflect questionsmentioned by Johnson, Bridson, de la Harpe in the literature in late $1990$sabout possibility of such embeddings for $\mathbb{Q}$. Technique used here isbased on the methods with integer-valued sequences sets used by Higman, andwith specific free constructions of groups, including free product withamalgamation, HNN-extension, an auxiliary technical structure of$*$-construction, etc.

On explicit embeddings of $\mathbb{Q}$ into finitely presented groups