In mathematics, especially in the area of algebra known as group theory, the Prüfer rank of a pro-p group measures the size of a group in terms of the ranks of its elementary abelian sections.
[1] The rank is well behaved and helps to define analytic pro-p-groups.
will be equal to the size of any minimal generating set of
Those profinite groups with finite Prüfer rank are more amenable to analysis.
Specifically in the case of finitely generated pro-p groups, having finite Prüfer rank is equivalent to having an open normal subgroup that is powerful.
In turn these are precisely the class of pro-p groups that are p-adic analytic – that is groups that can be imbued with a p-adic manifold structure.