The Diophantine problem in Thompson's group F

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Elliott, Luna and Levine, Alex (2025) The Diophantine problem in Thompson's group F. (In Press)

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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 B\"uchi and Senger and Ciobanu and Garreta to show the Diophantine problem in free groups and monoids with abelianisation constraints is undecidable.

Item Type:	Article
Additional Information:	10 pages, thanks to James Belk and Corentin Bodart for pointing out that F is a centralizer in T, thanks to anonymous referee for helpful comments
Uncontrolled Keywords:	math.gr,11d72, 20f65
Faculty \ School:	Faculty of Science > School of Engineering, Mathematics and Physics
UEA Research Groups:	Faculty of Science > Research Groups > Algebra, Number Theory, Logic, and Representations (ANTLR)
Related URLs:	http://arxiv.org/pdf/2502.14970v3
Depositing User:	LivePure Connector
Date Deposited:	29 Apr 2025 17:30
Last Modified:	29 Apr 2025 17:30
URI:	https://ueaeprints.uea.ac.uk/id/eprint/99152
DOI:

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