Algebra

Results named in Tau Ceti's TauCeti.Topology.Algebra modules and in no roadmap's section, as Tau Ceti has them at commit ace60277.

The abelianization structure… to Structure theorem for…

• The abelianization structure theorem for one-relator pro-p groups
• Burnside's basis theorem, cardinal form
• Burnside's criterion modulo λ_1
• Burnside's surjectivity criterion
• The existence theorem of the classification for odd rank, as an equivalence (Labute, Theorem 1 and Remark 2; Serre, Theorem 3.2)
• The existence theorem of the classification of Demushkin groups for even rank, as an equivalence (Labute, Theorem 1 and Remark 2; Serre, Theorem 3.2)
• The first isomorphism theorem for a surjective strict homomorphism of topological groups
• The Frattini criterion for a kernel
• Gaschütz's lifting lemma for profinite groups
• Henkel's open mapping theorem
• Henkel's theorem in quotient form
• Labute's Theorem 2 at the even-rank dyadic endpoint
• Labute's Theorem 4: a Demushkin group has exactly one continuous character with the prescription property
• Lagrange's theorem for profinite groups
• Lyndon's theorem for the relation module (NSW (5.6.6))
• Macbeath's theorem
• Nakayama's lemma for pro-p groups
• The open Frattini criterion
• The Schreier bound
• Structure theorem for topologically finitely generated abelian pro-p groups

Structure theorem for… to The two-term Euler formula

• Structure theorem for torsion-free topologically finitely generated abelian pro-p groups
• The successive-approximation theorem with tails
• Tate's criterion for the cohomological dimension of a pro-p group
• Tate's duality criterion for cd_p G ≤ 2
• The three-term Euler formula
• The three-term Euler identity under cd_p G ≤ 2
• The topological first isomorphism theorem for rings
• The topological Nakayama lemma
• The torsion-free case of the structure theorem
• The trivial-filtration theorem
• The two-term Euler formula

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