Embedding Q into a finitely presented group

Belk, J. , Hyde, J. and Matucci, F. (2022) Embedding Q into a finitely presented group. Bulletin of the American Mathematical Society, 59, pp. 561-567. (doi: 10.1090/bull/1762)

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We observe that the group of all lifts of elements of Thompson's group <i>T</i> to the real line is finitely presented and contains the additive group Q of the rational numbers. This gives an explicit realization of the Higman embedding theorem for Q, answering a Kourovka notebook question of Martin Bridson and Pierre de la Harpe.

Item Type:Articles
Additional Information: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 Funda¸c˜ao para a Ciˆencia e a Tecnologia (CEMAT-Ciˆencias FCT projects UIDB/04621/2020 and UIDP/04621/2020) and of the Universit`a degli Studi di Milano–Bicocca (FA project ATE-2016-0045 “Strutture Algebriche”).
Glasgow Author(s) Enlighten ID:Belk, Dr Jim
Authors: Belk, J., Hyde, J., and Matucci, F.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Bulletin of the American Mathematical Society
Publisher:American Mathematical Society
ISSN (Online):1088-9485
Published Online:11 August 2022
Copyright Holders:Copyright © 2022 American Mathematical Society
First Published:First published in Bulletin of the American Mathematical Society 59: 561-567
Publisher Policy:Reproduced in accordance with the publisher copyright policy
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