Theorems · Theorem · group theory
groupCohomology.H1InfRes_exact
∀ {k G : Type u} [inst : CommRing k] [inst_1 : Group G] (A : Rep.{u, u, u} k G) (S : Subgroup G) [inst_2 : S.Normal],
(groupCohomology.H1InfRes A S).ExactGiven a G-representation A and a normal subgroup S ≤ G, the short complex
H¹(G ⧸ S, A^S) ⟶ H¹(G, A) ⟶ H¹(S, A) is exact.
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- Foundations
- Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingGroupSubgroup.Normal
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