Theorems · Theorem · group theory
Subgroup.map_commutator
∀ {G : Type u_1} {G' : Type u_2} [inst : Group G] [inst_1 : Group G'] (H₁ H₂ : Subgroup G) (f : G →* G'),
Subgroup.map f ⁅H₁, H₂⁆ = ⁅Subgroup.map f H₁, Subgroup.map f H₂⁆- Defined in
- Mathlib.GroupTheory.Commutator.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- SetLike.coeproof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- Bracket.bracketstatement and proof · cited by 642
- Subgroup.mapstatement and proof · cited by 301
- Subgroup.commutator_mem_commutatorproof · cited by 13
- Subgroup.mem_map_of_memproof · cited by 5
- map_commutatorElementproof · cited by 4
Cited by12
Results whose statement or proof uses this declaration.
- Subgroup.map_subtype_commutatorproof · cited by 7
- Subgroup.map_lowerCentralSeriesproof · cited by 4
- Group.IsSolvable.commutator_lt_of_ne_botproof · cited by 2
- Subgroup.commutator_le_map_commutatorproof · cited by 2
- map_derivedSeries_le_derivedSeriesproof · cited by 2
- IsZGroup.isCyclic_commutatorproof · cited by 1
- Subgroup.commutator_pi_pi_of_finiteproof · cited by 1
- Subgroup.commutator_prod_prodproof · cited by 1
- Group.isSolvable_iff_commutator_ltproof · cited by 1
- Group.IsPerfect.mapproof · cited by 1
- map_commutator_eqproof · cited by 0
- alternatingGroup.kleinFour_eq_commutatorproof · cited by 0