Pro-p group

In mathematics, a pro-p group (for some prime number p) is a profinite group ${\displaystyle G}$ such that for any open normal subgroup ${\displaystyle N\triangleleft G}$ the quotient group ${\displaystyle G/N}$ is a p-group. Note that, as profinite groups are compact, the open subgroups are exactly the closed subgroups of finite index, so that the discrete quotient group is always finite.

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