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Theorems · Theorem · group theory

AddGroup.fg_iff_addMonoid_fg

∀ {G : Type u_3} [inst : AddGroup G], AddGroup.FG G ↔ AddMonoid.FG G

An additive group is finitely generated if and only if it is finitely generated as an additive monoid.

Defined in
Mathlib.GroupTheory.Finiteness
Cited by
2 results in Mathlib
Foundations
Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddGroup
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AddGroup.fg_of_surjective · cited by 2AddGroup.fg_of_surjectiveAddGroup.fg_iff_addSubgroup_fg · cited by 2AddGroup.fg_iff_addSubgro…Top.top · cited by 9680Top.topAddGroup · cited by 4410AddGroupAddGroup.FG · cited by 37AddGroup.FGAddMonoid.FG · cited by 31AddMonoid.FGAddMonoid.fg_def · cited by 6AddMonoid.fg_defAddSubgroup.fg_iff_addSubmonoid_fg · cited by 6AddSubgroup.fg_iff_addSub…AddGroup.fg_def · cited by 3AddGroup.fg_defAddGroup.fg_iff_addMonoid_fgCITED BYCITES

Cites7

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Cited by2

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