4 problems

A group $G$ is parafree if it is residually nilpotent and has the same nilpotent quotients as some free group. Baumslag's Parafree Conjecture. Every finitely generated parafree gro…

Let $G$ be a residually nilpotent group. Write $H_1(G)$ and $H_2(G)$ for its integral first and second homology groups, and let $\operatorname{Hom}(H_2(G),\mathbb Z)$ denote the gr…

A group $G$ is parafree if it is residually nilpotent and has the same nilpotent quotients as some free group. The Strong Parafree Conjecture. Every finitely generated parafree gro…

Let $F$ be a non-cyclic free group, and let $\widehat F$ denote its free pronilpotent completion. For a group $G$, write $H_2(G)$ for its integral second homology and…