5 problems

Friedl–Löh conjecture. The uniform epimorphism problem onto the class of all finitely generated virtually abelian groups is not decidable.

Undecidability conjecture. The uniform epimorphism problem onto the class of all finitely generated virtually Abelian groups is not decidable.

Let $G$ be a finitely generated virtually abelian group, and let $\operatorname{rank} G$ denote its rank. Write $\mathcal{D}_{G,S}^{lin}(n)$ for the linear sofic profile of $G$ rel…

Let $G$ be a finitely generated group, and let $X$ be a finite generating set. Define the degree of commutativity with respect to $X$ by … Here $\mathbb{B}_X(n)$ is the ball of rad…

Let $G$ be a group, let $\{\mu_n\}_{n\in \mathbb{N}}$ be a sequence of “reasonable” measures on $G$, and let $\mathcal{E}\subseteq F_k$ be a set of equations in $k$ variables. The…