3 problems

Let $G$ be a group with exponential growth, and let $\varphi:G\longrightarrow G$ be an injective group endomorphism. The Reidemeister number $R(\varphi)$ is the number of $\varphi$…

Let $G$ be a finitely generated residually finite non-amenable group. Non-amenable property $R_\infty$ conjecture. The group $G$ has property $R_\infty$. This is presented as a wea…

Let $G$ be a finitely generated residually finite group. Fel'shtyn–Troitsky conjecture. The group $G$ either has property $R_\infty$ or is solvable-by-finite. The disjunction is no…