14.94 (1999)

For each positive integer $r$ find the $p$-cohomological dimension $\operatorname{cd}_p(H_r)$ where $H_r$ is the closed subgroup of $N(\mathbb{Z}/p\mathbb{Z})$ consisting of the series $\displaystyle x \left( 1 + \sum_{i=1}^\infty a_i x^{p^{r_i}} \right)$, $a_i \in \mathbb{Z}/p\mathbb{Z}$.