Let $G$ be a profinite group of $p$-cohomological dimension, $cd_p(G)\neq 0,\infty$. Consider an open subgroup $U\leq G$. Does there exist an open subgroup $V\leq U$ such that its index, $[U:V]$ is divisible by $p$?
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2025-01-13 05:50:39.1736747439
Open subgroups $V\subset U$ of profinite group such that the index $[U:V]$ is divisible by $p$.
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