Theorems · Theorem · group theory
MulAction.stabilizer_smul_eq_stabilizer_map_conj
∀ {G : Type u_1} {α : Type u_2} [inst : Group G] [inst_1 : MulAction G α] (g : G) (a : α),
MulAction.stabilizer G (g • a) = Subgroup.map (MulEquiv.toMonoidHom (MulAut.conj g)) (MulAction.stabilizer G a)If the stabilizer of a is S, then the stabilizer of g • a is gSg⁻¹.
- Defined in
- Mathlib.GroupTheory.GroupAction.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
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Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement · cited by 3,629
- Subgroupstatement · cited by 3,593
- one_smulproof · cited by 1,374
- MulActionstatement and proof · cited by 1,294
- smul_smulproof · cited by 360
- Subgroup.mapstatement and proof · cited by 301
- MulAction.stabilizerstatement and proof · cited by 254
- MulAutstatement · cited by 158
- MulEquiv.toMonoidHomstatement and proof · cited by 126
- Subgroup.extproof · cited by 108
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