4 problems

Open-subgroup triviality conjecture. If

Solvable-radical sequence conjecture. There exists a sequence $u_n(x,y)$ such that $R(G)$ coincides with the set of elements $y\in G$ having the property that, for every $x\in G$,…

Finite generation conjecture. If

Let $w$ be a group word and let $G$ be a profinite group such that every $w$-value in $G$ has finite order. Local finiteness conjecture. The verbal subgroup $w(G)$ is locally finit…