Theorems · Theorem · group theory

alternatingGroup.subgroup_eq_top_of_isPreprimitive

∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α],
  4 < Nat.card α →
    ∀ (G : Subgroup ↥(alternatingGroup α)) [hG' : MulAction.IsPreprimitive (↥G) α] {s : Set α},
      MulAction.stabilizer (↥(alternatingGroup α)) s ≤ G → G = ⊤

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 MulAction.IsPreprimitive

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Cites27

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
Top.topstatement · cited by 9,680
Fintypestatement and proof · cited by 7,736
MonoidHomproof · cited by 3,629
Subgroupstatement and proof · cited by 3,593
Equiv.Permstatement and proof · cited by 1,375
Nat.cardstatement and proof · cited by 844
Subgroup.mapproof · cited by 301
MulAction.stabilizerstatement and proof · cited by 254
eq_top_iffproof · cited by 236
Subgroup.subtypeproof · cited by 185

Cited by1

Results whose statement or proof uses this declaration.

alternatingGroup.isCoatom_stabilizer_of_ncard_lt_ncard_complproof · cited by 1