Theorems · Theorem · group theory
Subgroup.relIndex_inter_ne_zero
∀ {G : Type u_1} [inst : Group G] {J K : Subgroup G},
J.relIndex K ≠ 0 → ∀ (L : Subgroup G), (J ⊓ L).relIndex (K ⊓ L) ≠ 0If J has finite index in K, then J ⊓ L has finite index in K ⊓ L for any L.
- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
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Cites14
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- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- MonoidHom.rangeproof · cited by 314
- Subgroup.mapproof · cited by 301
- Subgroup.subtypeproof · cited by 185
- Subgroup.comapproof · cited by 154
- inf_commproof · cited by 139
- Subgroup.relIndexstatement and proof · cited by 72
- Subgroup.range_subtypeproof · cited by 28
- Subgroup.subtype_injectiveproof · cited by 18
- Subgroup.relIndex_comapproof · cited by 7
- Subgroup.comap_map_eq_self_of_injectiveproof · cited by 7
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