Theorems · Definition · group theory
unitsCentralizerEquiv
(M : Type u_2) →
[inst : Monoid M] → (x : Mˣ) → (↥(Submonoid.centralizer {↑x}))ˣ ≃* ↥(MulAction.stabilizer (ConjAct Mˣ) x)The stabilizer of Mˣ acting on itself by conjugation at x : Mˣ is exactly the
units of the centralizer of x : M.
- Defined in
- Mathlib.GroupTheory.GroupAction.ConjAct
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Quot.sound
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Monoidstatement and proof · cited by 3,887
- Subgroupstatement · cited by 3,593
- Submonoidstatement · cited by 3,086
- Unitsstatement and proof · cited by 2,804
- Units.valstatement and proof · cited by 1,966
- MulEquivstatement · cited by 1,142
- MulEquiv.symmproof · cited by 482
- MulAction.stabilizerstatement and proof · cited by 254
- Units.mapproof · cited by 95
- ConjActstatement and proof · cited by 79
Cited by2
Results whose statement or proof uses this declaration.
- val_unitsCentralizerEquiv_apply_coestatement and proof · cited by 0
- val_unitsCentralizerEquiv_symm_apply_coestatement and proof · cited by 0