Theorems · Definition · group theory
AddAction.toPermHom
(G : Type u_1) → (α : Type u_5) → [inst : AddGroup G] → [AddAction G α] → G →+ Additive (Equiv.Perm α)
Given an action of an additive group G on a set α, each g : G defines a permutation of
α.
- Defined in
- Mathlib.Algebra.Group.Action.End
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- AddGroupstatement and proof · cited by 4,410
- AddMonoidHomstatement · cited by 3,230
- Equiv.Permstatement · cited by 1,375
- Multiplicativeproof · cited by 875
- AddActionstatement and proof · cited by 820
- Additivestatement · cited by 356
- MulAction.toPermHomproof · cited by 16
- MonoidHom.toAdditiveRightproof · cited by 9
Cited by3
Results whose statement or proof uses this declaration.
- AddAction.coe_toPermHomstatement · cited by 0
- AddAction.toPermHom_apply_applystatement and proof · cited by 0
- AddAction.toPermHom_apply_symm_applystatement and proof · cited by 0