Theorems · Theorem · group theory
Subgroup.exists_smul_eq
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G} [inst_1 : IsMulCommutative ↥H] [inst_2 : H.FiniteIndex]
[inst_3 : H.Normal], (Nat.card ↥H).Coprime H.index → ∀ (α β : H.QuotientDiff), ∃ h, h • α = β- Defined in
- Mathlib.GroupTheory.SchurZassenhaus
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Groupstatement and proof · cited by 6,238
- Equiv.symmproof · cited by 3,681
- Subgroupstatement and proof · cited by 3,593
- Nat.cardstatement and proof · cited by 844
- MulOpposite.opproof · cited by 520
- Equiv.apply_symm_applyproof · cited by 346
- Subgroup.Normalstatement and proof · cited by 334
- MonoidHom.idproof · cited by 323
- Subgroup.indexstatement and proof · cited by 150
- inv_powproof · cited by 140
- mul_inv_cancelproof · cited by 128
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.isComplement'_stabilizer_of_coprimeproof · cited by 0