Theorems · Inductive type · group theory
AddGroup.ResiduallyFinite
(G : Type u_1) → [AddGroup G] → Prop
An additive group G is residually finite if the intersection of all finite index normal
additive subgroups is trivial.
- Defined in
- Mathlib.GroupTheory.ResiduallyFinite
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- AddGroup
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.
- AddGroupstatement · cited by 4,410
Cited by14
Results whose statement or proof uses this declaration.
- AddGroup.residuallyFinite_iff_forall_finiteIndexNormalAddSubgroupstatement · cited by 4
- AddGroup.exists_finiteIndexNormalAddSubgroup_notMemstatement and proof · cited by 1
- AddGroup.ResiduallyFinite.iInf_eq_botstatement and proof · cited by 1
- AddGroup.residuallyFinite_defstatement and proof · cited by 1
- AddGroup.residuallyFinite_iff_exists_finiteIndexstatement · cited by 1
- AddGroup.residuallyFinite_iff_exists_finiteIndexNormalAddSubgroupstatement · cited by 1
- AddGroup.residuallyFinite_iff_forall_finiteIndexstatement · cited by 1
- ProfiniteAddGrp.ProfiniteCompletion.mono_eta_iff_residuallyFinitestatement and proof · cited by 1
- AddGroup.eq_zero_iff_forall_finiteIndexNormalSubroupstatement and proof · cited by 0
- AddGroup.exists_finiteIndexNormalAddSubgroup_of_residuallyFinitestatement and proof · cited by 0
- AddGroup.ResiduallyFinite.casesOnstatement and proof · cited by 0
- AddGroup.ResiduallyFinite.recOnstatement and proof · cited by 0