Theorems · Definition · group theory
SemidirectProduct.monoidHomSubgroup
{G : Type u_2} →
[inst : Group G] →
{H K : Subgroup G} →
(h : K ≤ Subgroup.normalizer ↑H) → ↥H ⋊[H.normalizerMonoidHom.comp (Subgroup.inclusion h)] ↥K →* GThe homomorphism from a semidirect product of subgroups to the ambient group.
- Defined in
- Mathlib.GroupTheory.SemidirectProduct
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 34 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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 · cited by 469
- Subgroup.subtypeproof · cited by 185
- MulAutstatement · cited by 158
- Subgroup.normalizerstatement and proof · cited by 108
- SemidirectProductstatement · cited by 69
- Subgroup.inclusionstatement · cited by 21
- Subgroup.normalizerMonoidHomstatement · cited by 10
- SemidirectProduct.liftproof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- SemidirectProduct.mulEquivSubgroupproof · cited by 3
- SemidirectProduct.mulEquivSubgroup_symm_applystatement · cited by 0
- SemidirectProduct.monoidHomSubgroup_applystatement and proof · cited by 0