Theorems · Theorem · group theory
Group.residuallyFinite_iff_forall_finiteIndexNormalSubgroup
∀ {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
- 3 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- iInfproof · cited by 1,690
- FiniteIndexNormalSubgroupstatement and proof · cited by 27
- FiniteIndexNormalSubgroup.toSubgroupproof · cited by 15
- Group.ResiduallyFinitestatement · cited by 12
Cited by3
Results whose statement or proof uses this declaration.
- ProfiniteGrp.ProfiniteCompletion.mono_eta_iff_residuallyFiniteproof · cited by 1
- Group.eq_one_iff_forall_finiteIndexNormalSubroupproof · cited by 0
- Group.residuallyFinite_iff_forall_finiteIndexproof · cited by 0