Theorems · Theorem · group theory
MonoidHom.map_zpow
∀ {α : Type u_2} {β : Type u_3} [inst : Group α] [inst_1 : DivisionMonoid β] (f : α →* β) (g : α) (n : ℤ),
f (g ^ n) = f g ^ nGroup homomorphisms preserve integer power.
- Defined in
- Mathlib.Algebra.Group.Hom.Defs
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses no axioms
- Assumes
- GroupDivisionMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- DivisionMonoidstatement and proof · cited by 201
- map_zpowproof · cited by 16
Cited by10
Results whose statement or proof uses this declaration.
- Units.val_zpow_eq_zpow_valproof · cited by 7
- DirichletCharacter.conductor_zpow_dvdproof · cited by 2
- MonoidHom.isMulCommutative_of_isCyclic_of_ker_le_centerproof · cited by 1
- CategoryTheory.GrpObj.zpow_compproof · cited by 1
- Pi.mulSingle_zpowproof · cited by 1
- star_zpowproof · cited by 1
- AddChar.map_zsmul_eq_zpowproof · cited by 0
- DilationEquiv.ratio_zpowproof · cited by 0
- AffineEquiv.constVAdd_zsmulproof · cited by 0
- MulChar.ringHomComp_zpowproof · cited by 0