One variable equations over the lamplighter group
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914173751918592 |
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| author | Ushakov, Alexander Wang, Yankun |
| author_facet | Ushakov, Alexander Wang, Yankun |
| contents | We prove that one variable equations in the lamplighter group $\MZ_2\wr \MZ$ are decidable and describe an algorithm for solving such equations. The algorithm has super-exponential time complexity in the worst case. We also show that, for most equations, decidability can be determined in nearly quadratic time; that is, the problem admits a nearly quadratic-time solution in the generic case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_23006 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | One variable equations over the lamplighter group Ushakov, Alexander Wang, Yankun Group Theory Combinatorics We prove that one variable equations in the lamplighter group $\MZ_2\wr \MZ$ are decidable and describe an algorithm for solving such equations. The algorithm has super-exponential time complexity in the worst case. We also show that, for most equations, decidability can be determined in nearly quadratic time; that is, the problem admits a nearly quadratic-time solution in the generic case. |
| title | One variable equations over the lamplighter group |
| topic | Group Theory Combinatorics |
| url | https://arxiv.org/abs/2511.23006 |