A branch group with unsolvable conjugacy problem

Fuente: arXiv
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Main Authors: Bishop, Alex, Schesler, Eduard
Format: Preprint
Published: 2025
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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