Theorems · Theorem · group theory
MonoidHom.map_zpowers
∀ {G : Type u_1} [inst : Group G] {N : Type u_3} [inst_1 : Group N] (f : G →* N) (x : G),
Subgroup.map f (Subgroup.zpowers x) = Subgroup.zpowers (f x)- Cited by
- 5 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setproof · cited by 53,352
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- Subgroup.mapstatement and proof · cited by 301
- Subgroup.zpowersstatement and proof · cited by 204
- Subgroup.closureproof · cited by 196
- Set.image_singletonproof · cited by 174
- MonoidHom.map_closureproof · cited by 16
- Subgroup.zpowers_eq_closureproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- Subgroup.isCyclic_iff_exists_zpowers_eq_topproof · cited by 4
- Valuation.IsRankOneDiscrete.generator'_zpowers_eq_topproof · cited by 3
- IsCyclic.card_powMonoidHom_rangeproof · cited by 1
- IsPrimitiveRoot.map_rootsOfUnityproof · cited by 0
- NumberField.IsCMField.indexRealUnits_eq_two_iffproof · cited by 0