Theorems · Theorem · group theory
Subgroup.map_subtype_inj
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G} {K L : Subgroup ↥H},
Subgroup.map H.subtype K = Subgroup.map H.subtype L ↔ K = L- Defined in
- Mathlib.Algebra.Group.Subgroup.Ker
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 75 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.
Cites6
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
- Subgroupstatement and proof · cited by 3,593
- Subgroup.mapstatement · cited by 301
- Subgroup.subtypestatement · cited by 185
- Subgroup.subtype_injectiveproof · cited by 18
- Subgroup.map_injectiveproof · cited by 1
Cited by11
Results whose statement or proof uses this declaration.
- Valuation.IsRankOneDiscrete.generator'_zpowers_eq_topproof · cited by 3
- MonoidHom.ker_transferSylow_isComplement'proof · cited by 3
- Subgroup.isPerfect_iffproof · cited by 2
- Subgroup.isNilpotent_iff_lowerCentralSeriesproof · cited by 2
- Subgroup.focalSubgroupOf_eq_closureproof · cited by 1
- alternatingGroup.range_ofSubtypeproof · cited by 1
- Group.isSolvable_iff_commutator_ltproof · cited by 1
- Group.IsPerfect.top_iffproof · cited by 1
- Subgroup.nilpotencyClass_leproof · cited by 0
- alternatingGroup.closure_cycleType_eq_two_two_eq_topproof · cited by 0
- alternatingGroup.closure_isThreeCycles_eq_topproof · cited by 0