A Branch Group With Unsolvable Conjugacy Problem
Abstract
Abstract We prove that every finitely generated residually finite group $G$ can be embedded in a finitely generated branch group $\Gamma $ such that two elements in $G$ are conjugate in $G$ if and only if they are conjugate in $\Gamma $. 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 Šuniḱ.
Fields of Study & Subjects
Geometric and Algebraic Topology
Publication details
- Journal / source
- International Mathematics Research Notices
- Volume
- 2026
- Issue
- 7
- Publication date
- 17 March 2026
- Language
- EN