12 problems

A finitely generated group is a group generated by finitely many elements, and it has solvable word problem when there is an algorithm deciding whether any word in its generators r…

Let $\T_g$ be the Torelli group of a closed genus-$g$ surface. Torelli finite-presentation conjecture. The group $\T_g$ is finitely presented for $g\geq 4$. This is presented as a…

Coherence conjecture for semidirect sums with a one-dimensional Lie algebra. If

Lie-algebra Kropholler–Walsh–Wise conjecture. If

Boone--Higman conjecture. Every finitely generated group with solvable word problem embeds in a finitely presented simple group.

Let $G$ be a group acting faithfully on a set $S$. The twisted Brin–Thompson group $SV_G$ is associated to this action. An action is said to have type (A) when $G$ is finitely pres…

Conjecture. $BV_{n,r}(H)$ is finitely presented whenever $H$ is finitely presented.

Finite presentability conjecture. If $(W,S)$ is not 2-spherical, meaning that there exist $s,t\in S$ with $|st|=\infty$, then $G$ is never finitely presented.

Let $\Lambda$ be an ordered abelian group, and let $G$ be a finitely generated group acting freely on a $\Lambda$-tree; such a group is called $\Lambda$-free. KMS conjecture. Every…

A generalised Wilson group is an infinitely iterated wreath product of finite non-abelian simple permutation groups of the type considered in the paper. A profinite group is finite…

A finitely presented group is a group defined by finitely many generators and relations, and a torsion group is one in which every element has finite order. The corresponding quest…

Bounded presentation complexity conjecture. The number of relations required to present $\Gamma_n$ remains bounded as $n$ increases if and only if $H_{\Sigma}$ is finitely presente…