Theorems · Theorem · group theory
Group.eq_one_iff_forall_finiteIndexNormalSubroup
∀ {G : Type u_1} [inst : Group G] [Group.ResiduallyFinite G] (g : G),
(∀ (H : FiniteIndexNormalSubgroup G), g ∈ H) → g = 1- Defined in
- Mathlib.GroupTheory.ResiduallyFinite
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupGroup.ResiduallyFinite
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Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- FiniteIndexNormalSubgroupstatement and proof · cited by 27
- Group.ResiduallyFinitestatement and proof · cited by 12
- Group.residuallyFinite_iff_forall_finiteIndexNormalSubgroupproof · cited by 3
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