## Embedding $\mathbb {Q}$ into a finitely presented group

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James Belk, James Hyde and Francesco Matucci
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## Abstract:

We observe that the group of all lifts of elements of Thompson’s group $T$ to the real line is finitely presented and contains the additive group $\mathbb {Q}$ of the rational numbers. This gives an explicit realization of the Higman embedding theorem for $\mathbb {Q}$, answering a Kourovka notebook question of Martin Bridson and Pierre de la Harpe.## References

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## Additional Information

**James Belk**- Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853
- MR Author ID: 760112
- Email: jmb226@cornell.edu
**James Hyde**- Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853
- MR Author ID: 905762
- Email: jth263@cornell.edu
**Francesco Matucci**- Affiliation: Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano–Bicocca, Milan 20125, Italy
- MR Author ID: 788744
- ORCID: 0000-0003-4762-5684
- Email: francesco.matucci@unimib.it
- Received by editor(s): September 1, 2021
- Published electronically: August 11, 2022
- Additional Notes: The first author was partially supported by EPSRC grant EP/R032866/1 as well as the National Science Foundation under Grant No. DMS-1854367 during the creation of this paper. The third author is a member of the Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni (GNSAGA) of the Istituto Nazionale di Alta Matematica (INdAM) and gratefully acknowledges the support of the Fundação para a Ciência e a Tecnologia (CEMAT-Ciências FCT projects UIDB/04621/2020 and UIDP/04621/2020) and of the Università degli Studi di Milano–Bicocca (FA project ATE-2016-0045 “Strutture Algebriche”)
- © Copyright 2022 American Mathematical Society
- Journal: Bull. Amer. Math. Soc.
**59**(2022), 561-567 - MSC (2020): Primary 20F05; Secondary 57M07, 20E32
- DOI: https://doi.org/10.1090/bull/1762
- MathSciNet review: 4478033