Theorems · Theorem · group theory
SubMulAction.fixingSubgroup_smul_eq_fixingSubgroup_map_conj
∀ {M : Type u_1} {α : Type u_2} [inst : Group M] [inst_1 : MulAction M α] (s : Set α) (g : M),
fixingSubgroup M (g • s) = Subgroup.map (MulEquiv.toMonoidHom (MulAut.conj g)) (fixingSubgroup M s)The fixingSubgroup of g • s is the conjugate of the fixingSubgroup of s by g.
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- Foundations
- Depth 34 from the axioms · uses propext, Quot.sound
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement · cited by 3,629
- Subgroupstatement · cited by 3,593
- MulActionstatement and proof · cited by 1,294
- Set.smulSetstatement · cited by 608
- Subgroup.mapstatement · cited by 301
- MulAutstatement · cited by 158
- MulEquiv.toMonoidHomstatement · cited by 126
- fixingSubgroupstatement · cited by 83
- MulAut.conjstatement · cited by 64
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