7 problems

Integral dimension subgroup conjecture. For every group $G$ and every $i\geq 1$, one has

Boundary-limit conjecture. The inclusion

Dimension subgroup conjecture. The dimension subgroup series with respect to the integers coincides with the lower central series:

Let $F$ be a free group and let $R,S$ be arbitrary normal subgroups of $F$. For a subgroup $N$ of $F$, write $[?]$... Dimension subgroup conjecture. … This conjecture extends the p…

Generalized dimension subgroup conjecture. For every such choice, the quotient

Dimension subgroup conjecture. The integer dimension subgroups of a group coincide with its lower central series:

For a group $G$, let $\mathcal{D}_k(G)$ be its $k$th dimension subgroup over the integers, and let $\gamma_kG$ be the lower central series defined by $\gamma_1G=G$ and…