Theorems · Definition · group theory
zpowGroupHom
{α : Type u_1} → [inst : DivisionCommMonoid α] → ℤ → α →* αThe n-th power map (for an integer n) on a commutative group, considered as a group
homomorphism.
- Defined in
- Mathlib.Algebra.Group.Hom.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
- Assumes
- DivisionCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MonoidHomstatement · cited by 3,629
- DivisionCommMonoidstatement and proof · cited by 80
- mul_zpowproof · cited by 12
Cited by14
Results whose statement or proof uses this declaration.
- zpowGroupHom_applystatement and proof · cited by 4
- QuotientGroup.equivQuotientZPowOfEquivstatement · cited by 3
- QuotientGroup.homQuotientZPowOfHomstatement and proof · cited by 3
- Circle.isQuotientCoveringMap_zpowstatement and proof · cited by 1
- Multiset.prod_map_zpowproof · cited by 1
- smul_eq_self_of_preimage_zpow_eq_selfproof · cited by 0
- isQuotientCoveringMap_zpowstatement and proof · cited by 0
- ker_zpowGroupHom_eq_rootsOfUnitystatement · cited by 0
- QuotientGroup.equivQuotientZPowOfEquiv_reflstatement and proof · cited by 0
- QuotientGroup.equivQuotientZPowOfEquiv_symmstatement · cited by 0
- QuotientGroup.equivQuotientZPowOfEquiv_transstatement and proof · cited by 0
- QuotientGroup.homQuotientZPowOfHom_compstatement and proof · cited by 0