Theorems · Theorem · group theory
AddGroup.fg_iff_exists_freeAddGroup_hom_surjective
∀ {G : Type u_3} [inst : AddGroup G], AddGroup.FG G ↔ ∃ S, ∃ (_ : S.Finite), ∃ φ, Function.Surjective ⇑φAn additive group is finitely generated iff there exists a surjective homomorphism
from a FreeAddGroup on finitely many generators.
- Defined in
- Mathlib.GroupTheory.Finiteness
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 86 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.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Finsetproof · cited by 13,712
- Top.topproof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Set.Elemstatement and proof · cited by 7,166
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupproof · cited by 3,232
- AddMonoidHomstatement and proof · cited by 3,230
- Set.Finitestatement and proof · cited by 1,814
- Finset.finite_toSetproof · cited by 210
- AddSubgroup.closureproof · cited by 156
Cited by1
Results whose statement or proof uses this declaration.
- AddGroup.fg_iff_exists_freeAddGroup_hom_surjective_finiteproof · cited by 0