Theorems · Theorem · group theory
Subgroup.commutator_mono
∀ {G : Type u_1} [inst : Group G] {H₁ H₂ K₁ K₂ : Subgroup G}, H₁ ≤ K₁ → H₂ ≤ K₂ → ⁅H₁, H₂⁆ ≤ ⁅K₁, K₂⁆- Defined in
- Mathlib.GroupTheory.Commutator.Basic
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 71 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.
Cites5
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
- Bracket.bracketstatement · cited by 642
- Subgroup.commutator_mem_commutatorproof · cited by 13
- Subgroup.commutator_leproof · cited by 10
Cited by11
Results whose statement or proof uses this declaration.
- Subgroup.lowerCentralSeries_monoproof · cited by 5
- Subgroup.lowerCentralSeries_pi_leproof · cited by 2
- Subgroup.commutator_le_map_commutatorproof · cited by 2
- Sylow.le_center_or_le_commutatorproof · cited by 1
- Subgroup.commutator_pi_pi_of_finiteproof · cited by 1
- Subgroup.derived_le_lower_centralproof · cited by 1
- Subgroup.commutator_prod_prodproof · cited by 1
- alternatingGroup.commutator_perm_eqproof · cited by 1
- Sylow.normalizer_le_centralizer_or_le_commutatorproof · cited by 1
- Subgroup.Normal.of_commutator_leproof · cited by 0
- commutator_centralizer_commutator_le_centerproof · cited by 0