The Diophantine problem in Thompson’s group F

Elliott, Luna and Levine, Alex ORCID: https://orcid.org/0000-0001-9633-9313 (2025) The Diophantine problem in Thompson’s group F. Mathematics of Computation, 95 (360). pp. 2013-2023. ISSN 0025-5718

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Abstract

We show that the Diophantine problem in Thompson’s group F is undecidable. Our proof uses the facts that F has finite commutator width and rank 2 abelianisation, then uses similar arguments used by Büchi and Senger [Z. Math. Logik Grundlag. Math. 34 (1988), pp. 337–342] and Ciobanu and Garreta [Int. Math. Res. Not. IMRN 5 (2024), pp. 4119–4159] to show the Diophantine problem in free groups and monoids with abelianisation constraints is undecidable.

Item Type:	Article
Additional Information:	Publisher Copyright: © 2025 American Mathematical Society
Uncontrolled Keywords:	equations in groups,thompson’s group f,algebra and number theory,computational mathematics,applied mathematics ,/dk/atira/pure/subjectarea/asjc/2600/2602
Faculty \ School:	Faculty of Science > School of Engineering, Mathematics and Physics
Related URLs:	https://www.scopus.com/pages/publication...
Depositing User:	LivePure Connector
Date Deposited:	15 Sep 2026 08:01
Last Modified:	20 Sep 2026 05:28
URI:	https://ueaeprints.uea.ac.uk/id/eprint/104527
DOI:	10.1090/MCOM/4113

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