Theorems · Theorem · group theory
Subgroup.IsComplement.finite_right_iff
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G} {T : Set G},
Subgroup.IsComplement (↑H) T → (Finite ↑T ↔ H.FiniteIndex)A right transversal is finite iff the subgroup has finite index.
- Defined in
- Mathlib.GroupTheory.Complement
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- Set.Elemstatement · cited by 7,166
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Finitestatement and proof · cited by 3,029
- HasQuotient.Quotientproof · cited by 2,301
- Subgroup.FiniteIndexstatement and proof · cited by 113
- Subgroup.IsComplementstatement and proof · cited by 94
- Equiv.finite_iffproof · cited by 21
- Subgroup.finiteIndex_of_finite_quotientproof · cited by 6
- Subgroup.IsComplement.rightQuotientEquivproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.IsComplement.finite_rightproof · cited by 1