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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.14970 |
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| _version_ | 1866912333396180992 |
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| author | Elliott, Luna Levine, Alex |
| author_facet | Elliott, Luna Levine, Alex |
| contents | 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 and Ciobanu and Garreta to show the Diophantine problem in free groups and monoids with abelianisation constraints is undecidable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_14970 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Diophantine problem in Thompson's group F Elliott, Luna Levine, Alex Group Theory 11D72, 20F65 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 and Ciobanu and Garreta to show the Diophantine problem in free groups and monoids with abelianisation constraints is undecidable. |
| title | The Diophantine problem in Thompson's group F |
| topic | Group Theory 11D72, 20F65 |
| url | https://arxiv.org/abs/2502.14970 |