Theorems · Theorem · group theory
AddGroup.fg_iff_exists_freeAddGroup_hom_surjective_finite
∀ {G : Type u_3} [inst : AddGroup G], AddGroup.FG G ↔ ∃ α, ∃ (_ : Finite α), ∃ φ, Function.Surjective ⇑φAn additive group is finitely generated iff there exists a surjective homomorphism
from a FreeAddGroup on an arbitrary finite type α to the group.
- Defined in
- Mathlib.GroupTheory.Finiteness
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
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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
- Setproof · cited by 53,352
- Equivproof · cited by 8,337
- Set.Elemproof · cited by 7,166
- AddGroupstatement and proof · cited by 4,410
- AddMonoidHomstatement and proof · cited by 3,230
- Finitestatement and proof · cited by 3,029
- Set.Finiteproof · cited by 1,814
- AddEquiv.symmproof · cited by 530
- AddMonoidHom.compproof · cited by 339
- AddMonoidHomClass.toAddMonoidHomproof · cited by 232
- FreeAddGroupstatement and proof · cited by 90
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