Theorems · Theorem · group theory

Subgroup.leftTransversals.diff_inv

∀ {G : Type u_1} [inst : Group G] {H : Subgroup G} {A : Type u_2} [inst_1 : CommGroup A] (ϕ : ↥H →* A)
  (S T : H.LeftTransversal) [inst_2 : H.FiniteIndex],
  (Subgroup.leftTransversals.diff ϕ S T)⁻¹ = Subgroup.leftTransversals.diff ϕ T S

Defined in: Mathlib.GroupTheory.Transfer
Cited by: 2 results in Mathlib
Foundations: Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Group CommGroup Subgroup.FiniteIndex

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Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Groupstatement and proof · cited by 6,238
MonoidHomstatement and proof · cited by 3,629
Subgroupstatement and proof · cited by 3,593
CommGroupstatement and proof · cited by 990
Subgroup.FiniteIndexstatement and proof · cited by 113
inv_eq_of_mul_eq_one_rightproof · cited by 15
Subgroup.LeftTransversalstatement and proof · cited by 13
Subgroup.leftTransversals.diffstatement · cited by 8
Subgroup.leftTransversals.diff_mul_diffproof · cited by 3
Subgroup.leftTransversals.diff_selfproof · cited by 2

Cited by2

Results whose statement or proof uses this declaration.

Subgroup.eq_one_of_smul_eq_oneproof · cited by 1
Subgroup.exists_smul_eqproof · cited by 1