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Theorems · Theorem · group theory

IsAddTorsion.of_surjective

∀ {G : Type u_1} {H : Type u_2} [inst : AddGroup G] [inst_1 : AddGroup H] {f : G →+ H},
  Function.Surjective ⇑f → IsAddTorsion G → IsAddTorsion H

The image of a surjective torsion additive group homomorphism is torsion.

Defined in
Mathlib.GroupTheory.Torsion
Cited by
2 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Quot.sound
Assumes
AddGroupAddGroup
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Around this declaration

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

IsAddTorsion.quotient_iff · cited by 1IsAddTorsion.quotient_iffAddIsTorsion.of_surjective · cited by 0AddIsTorsion.of_surjectiveDFunLike.coe · cited by 62936DFunLike.coeAddGroup · cited by 4410AddGroupAddMonoidHom · cited by 3230AddMonoidHomIsAddTorsion · cited by 42IsAddTorsionAddMonoidHom.isOfFinAddOrder · cited by 2AddMonoidHom.isOfFinAddOr…IsAddTorsion.of_surjectiveCITED BYCITES

Cites5

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Cited by2

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