14.57 (1999)

Describe the hereditarily just infinite pro-$p$-groups of finite width.

Definitions: A pro-$p$-group $G$ has finite width $p^d$ if $\lvert \gamma_i(G)/\gamma_{i+1}(G) \rvert \leqslant p^d$ for all $i$, and $G$ is hereditarily just infinite if $G$ is infinite and each of its open subgroups has no closed normal subgroups of infinite index.