Theorems · Definition · group theory

MulAction.stabilizerEquivStabilizerOfOrbitRel

{G : Type u_1} →
  {α : Type u_2} →
    [inst : Group G] →
      [inst_1 : MulAction G α] →
        {a b : α} → (MulAction.orbitRel G α) a b → ↥(MulAction.stabilizer G a) ≃* ↥(MulAction.stabilizer G b)

A isomorphism between the stabilizers of two elements in the same orbit.

Defined in: Mathlib.GroupTheory.GroupAction.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Group MulAction

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Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Groupstatement and proof · cited by 6,238
Subgroupstatement · cited by 3,593
MulActionstatement and proof · cited by 1,294
MulEquivstatement · cited by 1,142
MulEquiv.symmproof · cited by 482
MulAction.stabilizerstatement · cited by 254
MulAction.orbitRelstatement · cited by 114
MulAction.stabilizerEquivStabilizerproof · cited by 16

Cited by1

Results whose statement or proof uses this declaration.

MulAction.sigmaFixedByEquivOrbitsProdGroupproof · cited by 1