Theorems · Theorem · group theory
addCommutator_eq_bot_iff_center_eq_top
∀ (G : Type u_1) [inst : AddGroup G], addCommutator G = ⊥ ↔ AddSubgroup.center G = ⊤
- Defined in
- Mathlib.GroupTheory.Commutator.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 72 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- Bot.botstatement · cited by 4,720
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- top_le_iffproof · cited by 175
- Set.univ_subset_iffproof · cited by 49
- AddSubgroup.centerstatement and proof · cited by 40
- addCommutatorstatement · cited by 17
- AddSubgroup.addCommutator_eq_bot_iff_le_centralizerproof · cited by 7
- AddSubgroup.coe_eq_univproof · cited by 6
- AddSubgroup.centralizer_eq_top_iff_subsetproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- addCommutator_eq_bot_iffproof · cited by 1