Theorems · Theorem · group theory
addCommutator_centralizer_addCommutator_le_center
∀ (G : Type u_1) [inst : AddGroup G], ⁅AddSubgroup.centralizer ↑(addCommutator G), AddSubgroup.centralizer ↑(addCommutator G)⁆ ≤ AddSubgroup.center G
- Defined in
- Mathlib.GroupTheory.Commutator.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
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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
- Bot.botproof · cited by 4,720
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- Bracket.bracketstatement and proof · cited by 642
- le_topproof · cited by 411
- AddSubgroup.centerstatement · cited by 40
- AddSubgroup.centralizerstatement and proof · cited by 24
- addCommutatorstatement and proof · cited by 17
- AddSubgroup.addCommutator_eq_bot_iff_le_centralizerproof · cited by 7
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