Theorems · Theorem · group theory

Equiv.Perm.alternatingGroup_le_of_isPreprimitive

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

Defined in: Mathlib.GroupTheory.SpecificGroups.Alternating.MaximalSubgroups
Cited by: 0 results in Mathlib
Foundations: Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Fintype DecidableEq MulAction.IsPreprimitive

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Setstatement and proof · cited by 53,352
Fintypestatement and proof · cited by 7,736
Subgroupstatement and proof · cited by 3,593
Equiv.Permstatement and proof · cited by 1,375
Nat.cardstatement and proof · cited by 844
MulAction.stabilizerstatement and proof · cited by 254
alternatingGroupstatement and proof · cited by 96
Set.mulActionSetstatement · cited by 95
MulAction.IsPreprimitivestatement and proof · cited by 50
Equiv.Perm.IsThreeCycleproof · cited by 34
Equiv.Perm.IsThreeCycle.mem_alternatingGroupproof · cited by 5
Equiv.Perm.exists_mem_stabilizer_isThreeCycleproof · cited by 2

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