A branch group with unsolvable conjugacy problem
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908603325087744 |
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| author | Bishop, Alex Schesler, Eduard |
| author_facet | Bishop, Alex Schesler, Eduard |
| contents | We prove that every finitely generated residually finite group $G$ can be embedded in a finitely generated branch group $Γ$ such that two elements in $G$ are conjugate in $G$ if and only if they are conjugate in $Γ$. As an application we construct a finitely generated branch group with solvable word problem and unsolvable conjugacy problem and thereby answer a question of Bartholdi, Grigorchuk, and Šunik. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_12161 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A branch group with unsolvable conjugacy problem Bishop, Alex Schesler, Eduard Group Theory 20F10, 20E08 We prove that every finitely generated residually finite group $G$ can be embedded in a finitely generated branch group $Γ$ such that two elements in $G$ are conjugate in $G$ if and only if they are conjugate in $Γ$. As an application we construct a finitely generated branch group with solvable word problem and unsolvable conjugacy problem and thereby answer a question of Bartholdi, Grigorchuk, and Šunik. |
| title | A branch group with unsolvable conjugacy problem |
| topic | Group Theory 20F10, 20E08 |
| url | https://arxiv.org/abs/2509.12161 |