Theorems · Theorem · group theory
SemidirectProduct.monoidHomSubgroup_apply
∀ {G : Type u_2} [inst : Group G] {H K : Subgroup G} (h : K ≤ Subgroup.normalizer ↑H)
(a : ↥H ⋊[H.normalizerMonoidHom.comp (Subgroup.inclusion h)] ↥K),
(SemidirectProduct.monoidHomSubgroup h) a = ↑a.left * ↑a.right- Defined in
- Mathlib.GroupTheory.SemidirectProduct
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- SetLike.coestatement and proof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- MonoidHom.compstatement and proof · cited by 469
- MulAutstatement · cited by 158
- Subgroup.normalizerstatement and proof · cited by 108
- SemidirectProductstatement and proof · cited by 69
- SemidirectProduct.rightstatement · cited by 35
- SemidirectProduct.leftstatement · cited by 30
- Subgroup.inclusionstatement and proof · cited by 21
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