Theorems · Theorem · group theory
AddSubgroup.isFiniteRelIndex_map_nsmulAddMonoidHom_of_fg
∀ {A : Type u_1} [inst : AddCommGroup A] {B : AddSubgroup A},
B.FG → ∀ {n : ℕ}, n ≠ 0 → (AddSubgroup.map (nsmulAddMonoidHom n) B).IsFiniteRelIndex B- Defined in
- Mathlib.GroupTheory.FiniteAbelian.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroup
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.
- AddCommGroupstatement and proof · cited by 12,871
- AddSubgroupstatement and proof · cited by 3,232
- AddSubgroup.mapstatement and proof · cited by 189
- AddMonoidHom.rangeproof · cited by 142
- AddSubgroup.addSubgroupOfproof · cited by 87
- AddSubgroup.extproof · cited by 75
- AddSubgroup.FiniteIndexproof · cited by 66
- AddGroup.FGproof · cited by 37
- nsmulAddMonoidHomstatement and proof · cited by 24
- AddSubgroup.FGstatement and proof · cited by 21
- AddSubgroup.IsFiniteRelIndexstatement · cited by 17
- AddMonoidHom.mem_rangeproof · cited by 16
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.isFiniteRelIndex_of_map_linearMapMulLeft_leproof · cited by 0