Theorems · Theorem · group theory
Subgroup.coe_mul_of_left_le_normalizer_right
∀ {G : Type u_2} [inst : Group G] (H N : Subgroup G), H ≤ Subgroup.normalizer ↑N → ↑(H ⊔ N) = ↑H * ↑NThe carrier of H ⊔ N is just ↑H * ↑N (pointwise set product)
when H is a subgroup of the normalizer of N in G.
- Defined in
- Mathlib.Algebra.Group.Subgroup.Pointwise
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 74 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.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- mul_oneproof · cited by 3,885
- Subgroupstatement and proof · cited by 3,593
- mul_assocproof · cited by 1,667
- Set.mulstatement · cited by 297
- mul_inv_revproof · cited by 270
- Set.Subset.antisymmproof · cited by 213
- Subgroup.closureproof · cited by 196
- MulMemClass.mul_memproof · cited by 173
- Subgroup.normalizerstatement and proof · cited by 108
Cited by2
Results whose statement or proof uses this declaration.
- Subgroup.coe_mul_of_right_le_normalizer_leftproof · cited by 1
- Subgroup.mul_normalproof · cited by 0