4 problems

Let $G$ be an infinite primitive permutation group whose subdegrees are all finite, and let $(m_r)$ be its lower subdegree sequence. Permutation-ends conjecture. If $(m_r)$ grows e…

The Bieri–Stallings connectivity-at-infinity conjecture. For $n\geq 2$, the group $B_n$ is $(n-2)$-connected at infinity.

The one-ended subgroup characterization. The subgroup $H$ of the finitely generated group $G$ is 1-ended in $G$ if and only if for each splitting $A\ast_C B$ of $G$, where…

Let a P3R group be a finitely presented group whose universal cover is proper homotopy equivalent to a 3-manifold. An end is semi-stable when its fundamental pro-group at infinity…