Theorems · Theorem · group theory

alternatingGroup.isCoatom_stabilizer_singleton

∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α],
  3 ≤ Nat.card α →
    ∀ {s : Set α}, s.Nonempty → s.Subsingleton → IsCoatom (MulAction.stabilizer (↥(alternatingGroup α)) s)

Defined in: Mathlib.GroupTheory.SpecificGroups.Alternating.MaximalSubgroups
Cited by: 1 results in Mathlib
Foundations: Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Fintype DecidableEq

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites18

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

Setstatement and proof · cited by 53,352
Fintypestatement and proof · cited by 7,736
Subgroupstatement and proof · cited by 3,593
Set.Nonemptystatement and proof · cited by 2,627
Nontrivialproof · cited by 2,416
Equiv.Permstatement and proof · cited by 1,375
Nat.cardstatement and proof · cited by 844
Set.Subsingletonstatement and proof · cited by 276
MulAction.stabilizerstatement and proof · cited by 254
IsCoatomstatement and proof · cited by 114
alternatingGroupstatement and proof · cited by 96
Set.mulActionSetstatement · cited by 95

Cited by1

Results whose statement or proof uses this declaration.

alternatingGroup.isCoatom_stabilizerproof · cited by 1