Theorems · Theorem · group theory
SemidirectProduct.mulEquivSubgroup_apply
∀ {G : Type u_2} [inst : Group G] {H K : Subgroup G} [inst_1 : H.Normal] (h : H.IsComplement' K)
(a : ↥H ⋊[H.normalizerMonoidHom.comp (Subgroup.inclusion ⋯)] ↥K),
(SemidirectProduct.mulEquivSubgroup h) a = ↑a.left * ↑a.right- Defined in
- Mathlib.GroupTheory.SemidirectProduct
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupSubgroup.Normal
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Cites19
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- DFunLike.coestatement and proof · cited by 62,936
- Top.topstatement · cited by 9,680
- SetLike.coestatement · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- MulEquivstatement · cited by 1,142
- MonoidHom.compstatement and proof · cited by 469
- le_topstatement · cited by 411
- Subgroup.Normalstatement and proof · cited by 334
- MulAutstatement · cited by 158
- Subgroup.normalizerstatement · cited by 108
- SemidirectProductstatement and proof · cited by 69
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