Equations in wreath products
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917796191928320 |
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| author | Bartholdi, Laurent Dong, Ruiwen Pernak, Leon Wächter, Jan Philipp |
| author_facet | Bartholdi, Laurent Dong, Ruiwen Pernak, Leon Wächter, Jan Philipp |
| contents | We survey solvability of equations in wreath products of groups, and prove that the quadratic diophantine problem is solvable in wreath products of Abelian groups. We consider the related question of determining commutator width, and prove that the quadratic diophantine problem is also solvable in Baumslag's finitely presented metabelian group. This text is a short version of an extensive article by the first-named authors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04905 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equations in wreath products Bartholdi, Laurent Dong, Ruiwen Pernak, Leon Wächter, Jan Philipp Group Theory Formal Languages and Automata Theory Logic We survey solvability of equations in wreath products of groups, and prove that the quadratic diophantine problem is solvable in wreath products of Abelian groups. We consider the related question of determining commutator width, and prove that the quadratic diophantine problem is also solvable in Baumslag's finitely presented metabelian group. This text is a short version of an extensive article by the first-named authors. |
| title | Equations in wreath products |
| topic | Group Theory Formal Languages and Automata Theory Logic |
| url | https://arxiv.org/abs/2410.04905 |