On explicit embeddings of ℚ into finitely presented groups

2023/10/16 by Vahagn H. Mikaelian, Mikaelian, V. H.
Computer Science · Mathematics · #20E06 #20E07 #20F05 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2310.10536

openalex publication_date 2023/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Explicit embeddings of the group ℚ into a finitely presented group Q and into a 2-generator finitely presented group T_Q are suggested. The constructed embeddings reflect questions mentioned by Johnson, Bridson, de la Harpe in the literature in late 1990s about possibility of such embeddings for ℚ. Technique used here is based on the methods with integer-valued sequences sets used by Higman, and with specific free constructions of groups, including free product with amalgamation, HNN-extension, an auxiliary technical structure of *-construction, etc.

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