Theorems · Theorem · group theory
AddSubgroup.fg_iff_addSubmonoid_fg
∀ {G : Type u_3} [inst : AddGroup G] (P : AddSubgroup G), P.FG ↔ P.FGAn additive subgroup is finitely generated if and only if it is finitely generated as an additive submonoid.
- Defined in
- Mathlib.GroupTheory.Finiteness
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 83 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.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Finsetproof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- le_antisymmproof · cited by 2,068
- AddSubmonoidproof · cited by 1,178
- AddSubmonoid.closureproof · cited by 224
- Finset.finite_toSetproof · cited by 210
- AddSubgroup.closureproof · cited by 156
- AddSubgroup.toAddSubmonoidstatement and proof · cited by 91
- Set.Finite.unionproof · cited by 74
Cited by6
Results whose statement or proof uses this declaration.
- AddGroup.fg_iff_addMonoid_fgproof · cited by 2
- AddGroup.fg_iff_addSubgroup_fgproof · cited by 2
- AddSubgroup.fg_iff_mul_fgproof · cited by 1
- Subgroup.fg_iff_add_fgproof · cited by 1
- AddSubgroup.FG.piproof · cited by 0
- AddSubgroup.FG.prodproof · cited by 0