Theorems · Theorem · group theory
Subgroup.index_eq_one
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G}, H.index = 1 ↔ H = ⊤- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 95 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Subgroup.indexstatement and proof · cited by 150
- Nat.card_eq_one_iff_uniqueproof · cited by 15
- Subgroup.index_topproof · cited by 10
- QuotientGroup.subgroup_eq_top_of_subsingletonproof · cited by 1
Cited by9
Results whose statement or proof uses this declaration.
- Subgroup.relIndex_eq_oneproof · cited by 6
- Subgroup.exists_right_complement'_of_coprimeproof · cited by 2
- Equiv.Perm.alternatingGroup_le_of_index_le_twoproof · cited by 2
- IsPGroup.le_or_disjoint_of_coprimeproof · cited by 1
- Subgroup.index_dvd_two_iffproof · cited by 1
- Subgroup.normal_of_index_eq_oneproof · cited by 1
- NumberField.IsCMField.indexRealUnits_eq_two_iffproof · cited by 0
- Subgroup.one_lt_index_of_ne_topproof · cited by 0
- alternatingGroup.index_eq_oneproof · cited by 0