Theorems · Inductive type · group theory
Group.ResiduallyFinite
(G : Type u_1) → [Group G] → Prop
A group G is residually finite if the intersection of all finite index normal subgroups is
trivial.
- Defined in
- Mathlib.GroupTheory.ResiduallyFinite
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement · cited by 6,238
Cited by14
Results whose statement or proof uses this declaration.
- Group.residuallyFinite_iff_forall_finiteIndexNormalSubgroupstatement · cited by 3
- Group.ResiduallyFinite.iInf_eq_botstatement and proof · cited by 1
- Group.residuallyFinite_iff_exists_finiteIndexstatement · cited by 1
- Group.residuallyFinite_iff_exists_finiteIndexNormalSubgroupstatement · cited by 1
- ProfiniteGrp.ProfiniteCompletion.mono_eta_iff_residuallyFinitestatement and proof · cited by 1
- Group.exists_finiteIndexNormalSubgroup_notMemstatement and proof · cited by 1
- Group.ResiduallyFinite.casesOnstatement and proof · cited by 0
- Group.ResiduallyFinite.recOnstatement and proof · cited by 0
- Group.residuallyFinite_defstatement and proof · cited by 0
- Group.residuallyFinite_iff_forall_finiteIndexstatement · cited by 0
- Group.residuallyFinite_of_forall_exists_finite_monoidHomstatement · cited by 0
- ProfiniteGrp.ProfiniteCompletion.etaFn_injective_iff_residuallyFinitestatement · cited by 0