8 problems

Let $p$ be a prime, let $T_p$ be the rooted $p$-ary tree, and let $W_p$ be its full automorphism group. A pro-$p$ group is just-infinite if all its non-trivial closed normal subgro…

Finite-width conjecture. The ranks of the factors in the lower central series of $G$ are uniformly bounded; equivalently, the first Grigorchuk group has finite width.

Branch-group H-property conjecture. Many of these properties do not hold for groups from the other two classes.

A just infinite pro-$p$ group is a pro-$p$ group in which every proper quotient is finite, and a branch group is a just infinite pro-$p$ group of branch type. A nonabelian free pro…

Periodic Šunić-group conjecture. Every periodic Šunić group belongs to $\mathcal{MF}$.

Profinite closure conjecture. Every such subset is closed in the profinite topology.

Let $G$ be a branch group and let $W\leq G$ be a weakly maximal subgroup. Write $\NR(W)$ for the non-rigidity tree of $W$, and let $\partial\NR(W)$ denote its boundary. Minimality…

Let $G$ be a finitely generated, contracting, regular branch group, and let $(a_n)_{n=0}^{\infty}$ denote its portrait growth sequence. Portrait growth conjecture. The portrait gro…