Theorems · Definition · group theory
Subgroup.inclusion
{G : Type u_1} → [inst : Group G] → {H K : Subgroup G} → H ≤ K → ↥H →* ↥KThe inclusion homomorphism from a subgroup H contained in K to K.
- Defined in
- Mathlib.Algebra.Group.Subgroup.Defs
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- MonoidHom.mk'proof · cited by 3
Cited by28
Results whose statement or proof uses this declaration.
- Subgroup.card_dvd_of_leproof · cited by 5
- IsPGroup.to_leproof · cited by 5
- Subgroup.inclusion_injectivestatement · cited by 4
- SemidirectProduct.mulEquivSubgroupstatement · cited by 3
- Subgroup.isCyclic_of_leproof · cited by 3
- Subgroup.quotientSubgroupOfEmbeddingOfLEproof · cited by 3
- SubMulAction.ofFixingSubgroup_of_inclusionstatement · cited by 2
- SemidirectProduct.monoidHomSubgroupstatement · cited by 2
- Subgroup.inclusion_rangestatement · cited by 1
- SubMulAction.ofFixingSubgroup_of_inclusion_injectivestatement · cited by 1
- Subgroup.relIndex_subgroupOfproof · cited by 1
- IsPGroup.commutator_eq_bot_or_commutator_eq_selfproof · cited by 1