The Diophantine problem in Thompson's group F
Group Theory
2025-04-21 v3
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.
Keywords
Cite
@article{arxiv.2502.14970,
title = {The Diophantine problem in Thompson's group F},
author = {Luna Elliott and Alex Levine},
journal= {arXiv preprint arXiv:2502.14970},
year = {2025}
}
Comments
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