Theorems · Theorem · group theory
Subgroup.commutator_top_right_eq_bot_iff_le_center
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G}, ⁅H, ⊤⁆ = ⊥ ↔ H ≤ Subgroup.center G- Defined in
- Mathlib.GroupTheory.Commutator.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 72 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Top.topstatement · cited by 9,680
- Groupstatement and proof · cited by 6,238
- Bot.botstatement · cited by 4,720
- Subgroupstatement and proof · cited by 3,593
- Bracket.bracketstatement · cited by 642
- Subgroup.centerstatement and proof · cited by 121
- Subgroup.centralizerproof · cited by 65
- Subgroup.coe_topproof · cited by 8
- Subgroup.commutator_eq_bot_iff_le_centralizerproof · cited by 5
- Subgroup.centralizer_univproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Group.IsPerfect.upperCentralSeries_eq_centerproof · cited by 1
- Subgroup.commutator_top_left_eq_bot_iff_le_centerproof · cited by 0