Theorems · Theorem · group theory
AddSubgroup.addCommutator_eq_bot_iff_le_centralizer
∀ {G : Type u_1} [inst : AddGroup G] {H₁ H₂ : AddSubgroup G}, ⁅H₁, H₂⁆ = ⊥ ↔ H₁ ≤ AddSubgroup.centralizer ↑H₂- Defined in
- Mathlib.GroupTheory.Commutator.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
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.
- SetLike.coestatement and proof · cited by 8,199
- Bot.botstatement · cited by 4,720
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- Bracket.bracketstatement · cited by 642
- eq_bot_iffproof · cited by 159
- AddSubgroup.centralizerstatement and proof · cited by 24
- AddSubgroup.mem_botproof · cited by 18
- AddSubgroup.addCommutator_leproof · cited by 11
- addCommutatorElement_eq_zero_iff_add_commproof · cited by 3
Cited by7
Results whose statement or proof uses this declaration.
- addCommutator_eq_bot_iff_center_eq_topproof · cited by 1
- AddSubgroup.addCommutator_top_right_eq_bot_iff_le_centerproof · cited by 1
- AddSubgroup.addCommutator_addCommutator_eq_bot_of_rotateproof · cited by 1
- AddSubgroup.addCommutator_center_leftproof · cited by 0
- AddSubgroup.addCommutator_center_rightproof · cited by 0
- AddSubgroup.addCommutator_self_eq_bot_iffproof · cited by 0
- addCommutator_centralizer_addCommutator_le_centerproof · cited by 0