Profinite and pro-p groups

The declarations the status of Tau Ceti's roadmap names, and the other results named in the modules where only this status names declarations, or in folders below the areas where only it names 2 or more, as Tau Ceti has them at commit ace60277.

The classification of Demushkin… to The necessity half of the…

• The classification of Demushkin groups (Labute)
• Uniqueness of the dyadic Demushkin groups of even rank with image {±1} × U^(f) (Labute, Theorem 6)
• Tate's theorem: an infinite Demushkin group has p-cohomological dimension exactly 2
• Tate's duality map α₁ of an infinite Demushkin group with coefficients I(χ)/pⁱ is bijective on every finite discrete G-module M killed by pⁱ
• An open subgroup of an infinite Demushkin group is Demushkin (Serre's exposé, §9.2)
• The isomorphism type of an open subgroup of a Demushkin group
• Serre's theorem at arbitrary rank, as an equivalence
• The Golod–Shafarevich inequality
• The Demushkin predicate
• The unconstrained successive-approximation theorem
• TauCeti.profiniteFrattini
• Generation modulo the Frattini subgroup
• The constrained successive-approximation theorem
• The existence theorem of the classification for q ≠ 2, as an equivalence (Labute, Theorem 1 and Remark 2; Demushkin and Serre)
• The existence theorem of the classification of Demushkin groups, rank one (Labute, Remark 2 (iii); NSW (3.9.10))
• Labute's criterion
• Labute's Theorem 2
• Labute's Theorem 2 for q ≠ 2
• Labute's Theorem 2 for odd rank
• The necessity half of the existence theorem for q ≠ 2 (Labute, Theorem 1)

The relative…

• The relative successive-approximation theorem

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