Theorems · Theorem · group theory
Subgroup.normal_mul
∀ {G : Type u_2} [inst : Group G] (N H : Subgroup G) [N.Normal], ↑(N ⊔ H) = ↑N * ↑HThe carrier of N ⊔ H is just ↑N * ↑H (pointwise set product) when N is normal.
- Defined in
- Mathlib.Algebra.Group.Subgroup.Pointwise
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupSubgroup.Normal
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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 · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Subgroup.Normalstatement and proof · cited by 334
- Set.mulstatement · cited by 297
- Subgroup.le_normalizer_of_normalproof · cited by 3
- Subgroup.coe_mul_of_right_le_normalizer_leftproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- MonoidHom.ker_transferSylow_isComplement'proof · cited by 3