Theorems · Theorem · group theory
MulAction.isPreprimitive_stabilizer_of_surjective
∀ {M : Type u_1} {α : Type u_2} [inst : Group M] [inst_1 : MulAction M α] (s : Set α),
Function.Surjective MulAction.toPerm → MulAction.IsPreprimitive ↥(MulAction.stabilizer M s) ↑sIn the permutation group, the stabilizer of any set acts primitively on that set.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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 and proof · cited by 53,352
- Set.Elemstatement and proof · cited by 7,166
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- Equiv.Permstatement and proof · cited by 1,375
- MulActionstatement and proof · cited by 1,294
- Function.Bijectiveproof · cited by 863
- MulAction.stabilizerstatement and proof · cited by 254
- MulActionHomproof · cited by 124
- Set.mulActionSetstatement · cited by 95
- MulAction.IsPreprimitivestatement · cited by 50
Cited by2
Results whose statement or proof uses this declaration.
- MulAction.IsBlock.subsingleton_of_ssubset_of_stabilizer_leproof · cited by 2
- alternatingGroup.stabilizer_isPreprimitiveproof · cited by 1