Theorems · Theorem · group theory
MonoidHom.transfer_def
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G} {A : Type u_2} [inst_1 : CommGroup A] (ϕ : ↥H →* A)
(T : H.LeftTransversal) [inst_2 : H.FiniteIndex] (g : G), ϕ.transfer g = Subgroup.leftTransversals.diff ϕ T (g • T)- Defined in
- Mathlib.GroupTheory.Transfer
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- mul_commproof · cited by 2,262
- CommGroupstatement and proof · cited by 990
- Subgroup.FiniteIndexstatement and proof · cited by 113
- Subgroup.LeftTransversalstatement and proof · cited by 13
- Subgroup.leftTransversals.diffstatement and proof · cited by 8
- MonoidHom.transferstatement · cited by 6
- Subgroup.leftTransversals.diff_mul_diffproof · cited by 3
- Subgroup.leftTransversals.smul_diff_smulproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- MonoidHom.transfer_eq_prod_quotient_orbitRel_zpowers_quotproof · cited by 2