10 problems

Let $M$ be Churkin's group, the close variant of McKenzie's nilpotent group described above. Churkin's conjecture. The group $M$ is not a subgroup of any separable Hausdorff topolo…

Let $G\leq \mathrm{PL}_+ I$ be a finitely generated subgroup. An $F$-obstruction is a pair of elements of $G$ forming an $F$-obstruction in the sense of Theorem. Embedding conjectu…

Belk–Bleak–Matucci obstruction conjecture. The group $\mathbb{Z}^d*\mathbb{Z}$ is the correct obstruction for embeddability of right-angled Artin groups in $(d-1)V$.

Discreteness conjecture. The embeddings into $\operatorname{Cr}_3$ of $\mathcal{A}_6$ and $\operatorname{PSL}_2(7)$ up to conjugation form discrete families.

Let $\mathbb{F}$ be a free pro-$p$ group. Let the universal class of $\mathbb{Z}_p$ consist of the relevant $\mathbb{Z}_p$-rings in the language with constants, and let a fully res…

Let $A$ be a right-angled Artin group, and let $n$ be the number of complementary edges in its defining graph. Belk–Bleak–Matucci's conjecture. The group $A$ embeds into $(n-1)V$ i…

Let $\Delta$ and $\Gamma$ be simplicial graphs, and let $\mathbb{G}(\Delta)$ and $\mathbb{G}(\Gamma)$ be the corresponding partially commutative groups. The Tame Embedding Problem…

Let $\Gamma_1$ and $\Gamma_2$ be finite graphs. For a graph $\Gamma$, let $\Gamma^e$ denote its extension graph, whose vertices are conjugates of vertices of $\Gamma$, with adjacen…

Let $F_n$ be the free group of rank $n$, and let $\operatorname{Out}(F_n)$ denote its outer automorphism group. Bogopol'skii–Puga conjecture. For every positive integer $n$, there…

Let $(W,B)$ be a spherical latin bitrade, and let $\mathcal{A}_W^*$ and $\mathcal{A}_B^*$ denote the canonical abelian groups into which the white and black trades embed, respectiv…