Theorems · Theorem · group theory
commutator_centralizer_commutator_le_center
∀ (G : Type u_1) [inst : Group G], ⁅Subgroup.centralizer ↑(commutator G), Subgroup.centralizer ↑(commutator G)⁆ ≤ Subgroup.center G
- Defined in
- Mathlib.GroupTheory.Commutator.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
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Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Top.topproof · cited by 9,680
- SetLike.coestatement and proof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Bot.botproof · cited by 4,720
- Subgroupstatement and proof · cited by 3,593
- Bracket.bracketstatement and proof · cited by 642
- le_topproof · cited by 411
- Subgroup.centerstatement · cited by 121
- Subgroup.centralizerstatement and proof · cited by 65
- commutatorstatement and proof · cited by 56
- Set.centralizer_subsetproof · cited by 11
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