5 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…

Permutational Boone--Higman conjecture. Every finitely generated group with solvable word problem embeds in a group admitting an action of type $(\operatorname{A}_2)$; equivalently…

Higher finiteness-property conjecture. $SV_G$ is of type $\operatorname{\mathcal{F}}_n$ if and only if $G\curvearrowright S$ is of type $[\operatorname{A}_n]$.

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…