The Diophantine problem in Thompson's group F

Luna Elliott; Alex Levine

The Diophantine problem in Thompson's group F

Research output: Working paper › Preprint

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.

Original language	English
Publication status	Accepted/In press - 26 Apr 2025

Keywords

math.GR
11D72, 20F65

Access to Document

http://arxiv.org/pdf/2502.14970v3

Cite this

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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. ",

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