4 problems

Relative permutational Boone--Higman conjecture. Let $\Gamma$ be a finitely generated group with solvable word problem. Then there exists a group $G$ with a type…

Let a group $\Gamma$ act faithfully on a set $S$. The action is of type (A) if $\Gamma$ is finitely presented, every stabilizer $\operatorname{Stab}_{\Gamma}(s)$ is finitely genera…

Let $G$ be an oligomorphic group of permutations of a set $S$, and let $SV_G$ denote the associated twisted Brin–Thompson group. For $n\in\mathbb{N}$, write $\operatorname{F}_n$ fo…

Let $\Gamma$ be a finite simplicial graph, and let $A_\Gamma$ be the right-angled Artin group defined by generators corresponding to the vertices of $\Gamma$, with two generators c…