Theorems · Theorem · group theory
Subgroup.commute_of_normal_of_disjoint
∀ {G : Type u_1} [inst : Group G] (H₁ H₂ : Subgroup G),
H₁.Normal → H₂.Normal → Disjoint H₁ H₂ → ∀ (x y : G), x ∈ H₁ → y ∈ H₂ → Commute x yElements of disjoint, normal subgroups commute.
- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
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Cites14
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- SetLike.coeproof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Disjointstatement and proof · cited by 2,201
- mul_assocproof · cited by 1,667
- Commutestatement · cited by 639
- inv_invproof · cited by 494
- Subgroup.Normalstatement and proof · cited by 334
- mul_inv_revproof · cited by 270
- Disjoint.le_botproof · cited by 52
- Subgroup.inv_memproof · cited by 40
- Subgroup.mul_memproof · cited by 30
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