Theorems · Theorem · group theory
AddSubgroup.FG.prod
∀ {G : Type u_3} [inst : AddGroup G] {G' : Type u_5} [inst_1 : AddGroup G'] {P : AddSubgroup G} {Q : AddSubgroup G'},
P.FG → Q.FG → (P.prod Q).FGThe product of two finitely generated additive subgroups is finitely generated.
- Defined in
- Mathlib.GroupTheory.Finiteness
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
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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.prodstatement and proof · cited by 34
- AddSubgroup.FGstatement and proof · cited by 21
- AddSubgroup.fg_iff_addSubmonoid_fgproof · cited by 6
- AddSubmonoid.FG.prodproof · cited by 1
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