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- Pro-p_group abstract "In mathematics, a pro-p group (for some prime number p) is a profinite group such that for any open normal subgroup the quotient group 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.Alternatively, one can define a pro-p group to be the inverse limit of an inverse system of discrete finite p-groups.The best-understood (and historically most important) class of pro-p groups is the p-adic analytic groups: groups with the structure of an analytic manifold over such that group multiplication and inversion are both analytic functions.The work of Lubotzky and Mann, combined with Michel Lazard's solution to Hilbert's fifth problem over the p-adic numbers, shows that a pro-p group is p-adic analytic if and only if it has finite rank, i.e. there exists a positive integer such that any closed subgroup has a topological generating set with no more than elements.".
- Pro-p_group wikiPageID "1842075".
- Pro-p_group wikiPageRevisionID "562373816".
- Pro-p_group hasPhotoCollection Pro-p_group.
- Pro-p_group subject Category:Infinite_group_theory.
- Pro-p_group subject Category:P-groups.
- Pro-p_group subject Category:Topological_groups.
- Pro-p_group type Abstraction100002137.
- Pro-p_group type Group100031264.
- Pro-p_group type TopologicalGroups.
- Pro-p_group comment "In mathematics, a pro-p group (for some prime number p) is a profinite group such that for any open normal subgroup the quotient group is a p-group.".
- Pro-p_group label "Pro-p group".
- Pro-p_group sameAs m.06067q.
- Pro-p_group sameAs Q7246615.
- Pro-p_group sameAs Q7246615.
- Pro-p_group sameAs Pro-p_group.
- Pro-p_group wasDerivedFrom Pro-p_group?oldid=562373816.
- Pro-p_group isPrimaryTopicOf Pro-p_group.