Theorems · Theorem · group theory
AddGroup.fg_iff_addSubgroup_fg
∀ {G : Type u_3} [inst : AddGroup G] (H : AddSubgroup G), AddGroup.FG ↥H ↔ H.FG- Defined in
- Mathlib.GroupTheory.Finiteness
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 85 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.
Cites8
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
- AddSubgroupstatement and proof · cited by 3,232
- AddSubgroup.toAddSubmonoidproof · cited by 91
- AddGroup.FGstatement · cited by 37
- AddSubgroup.FGstatement · cited by 21
- AddSubgroup.fg_iff_addSubmonoid_fgproof · cited by 6
- AddMonoid.fg_iff_addSubmonoid_fgproof · cited by 3
- AddGroup.fg_iff_addMonoid_fgproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- AddSubgroup.isFiniteRelIndex_map_nsmulAddMonoidHom_of_fgproof · cited by 1
- AddSubgroup.IsFinitelyNormallyGenerated.of_FGproof · cited by 1