The results show that finitely generated groups can be represented in branched structures, highlighting the existence of groups with distinct problems.
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.
No takes yet. Share an insight, caveat, or question.
Bishop et al. (2025) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: