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Theorems · Theorem · group theory

isCyclic_of_injective

∀ {G : Type u_2} {G' : Type u_3} [inst : Group G] [inst_1 : Group G'] [IsCyclic G'] (f : G →* G'),
  Function.Injective ⇑f → IsCyclic G
Defined in
Mathlib.GroupTheory.SpecificGroups.Cyclic.Basic
Cited by
2 results in Mathlib
Foundations
Depth 49 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
GroupGroupIsCyclic
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Around this declaration

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

Subgroup.isCyclic_of_le · cited by 3Subgroup.isCyclic_of_leisZGroup_of_coprime · cited by 1isZGroup_of_coprimeDFunLike.coe · cited by 62936DFunLike.coeGroup · cited by 6238GroupMonoidHom · cited by 3629MonoidHomMulEquiv.symm · cited by 482MulEquiv.symmIsCyclic · cited by 122IsCyclicMulEquiv.surjective · cited by 41MulEquiv.surjectiveisCyclic_of_surjective · cited by 14isCyclic_of_surjectiveMonoidHom.ofInjective · cited by 12MonoidHom.ofInjectiveisCyclic_of_injectiveCITED BYCITES

Cites8

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Cited by2

Results whose statement or proof uses this declaration.