Theorems · Theorem · group theory
AddSubgroup.le_centralizer_iff_isAddCommutative
∀ {G : Type u_1} [inst : AddGroup G] {K : AddSubgroup G}, K ≤ AddSubgroup.centralizer ↑K ↔ IsAddCommutative ↥K- Defined in
- Mathlib.GroupTheory.Subgroup.Centralizer
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- IsAddCommutativestatement and proof · cited by 40
- AddSubgroup.centralizerstatement and proof · cited by 24
- add_comm'proof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- AddSubgroup.le_centralizerproof · cited by 0
- AddSubgroup.addCommutator_self_eq_bot_iffproof · cited by 0