Theorems · Theorem · group theory
AddGroup.residuallyFinite_iff_forall_finiteIndexNormalAddSubgroup
∀ {G : Type u_1} [inst : AddGroup G],
AddGroup.ResiduallyFinite G ↔ ∀ (g : G), (∀ (H : FiniteIndexNormalAddSubgroup G), g ∈ H) → g = 0- Defined in
- Mathlib.GroupTheory.ResiduallyFinite
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- iInfproof · cited by 1,690
- FiniteIndexNormalAddSubgroupstatement and proof · cited by 26
- FiniteIndexNormalAddSubgroup.toAddSubgroupproof · cited by 15
- AddGroup.ResiduallyFinitestatement · cited by 12
- AddSubgroup.eq_bot_iff_forallproof · cited by 11
- AddSubgroup.mem_iInfproof · cited by 4
- FiniteIndexNormalAddSubgroup.mem_toAddSubgroup_iffproof · cited by 1
- AddGroup.residuallyFinite_defproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- ProfiniteAddGrp.ProfiniteCompletion.mono_eta_iff_residuallyFiniteproof · cited by 1
- AddGroup.residuallyFinite_iff_exists_finiteIndexNormalAddSubgroupproof · cited by 1
- AddGroup.residuallyFinite_iff_forall_finiteIndexproof · cited by 1
- AddGroup.eq_zero_iff_forall_finiteIndexNormalSubroupproof · cited by 0