Theorems · Theorem · group theory

MulAction.IsBlock.subsingleton_of_ssubset_compl_of_stabilizer_alternatingGroup_le

∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α] {s B : Set α} {G : Subgroup ↥(alternatingGroup α)},
  s.Nontrivial → B ⊂ sᶜ → MulAction.stabilizer (↥(alternatingGroup α)) s ≤ G → MulAction.IsBlock (↥G) B → B.Subsingleton

Defined in: Mathlib.GroupTheory.SpecificGroups.Alternating.MaximalSubgroups
Cited by: 1 results in Mathlib
Foundations: Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Fintype DecidableEq

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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
Set.Elemproof · cited by 7,166
Subgroupstatement and proof · cited by 3,593
Compl.complstatement and proof · cited by 2,925
Equiv.Permstatement and proof · cited by 1,375
Set.Subsingletonstatement · cited by 276
MulAction.stabilizerstatement and proof · cited by 254
compl_complproof · cited by 229
Set.Nontrivialstatement and proof · cited by 145
alternatingGroupstatement and proof · cited by 96
Set.mulActionSetstatement · cited by 95

Cited by1

Results whose statement or proof uses this declaration.

alternatingGroup.isCoatom_stabilizer_of_ncard_lt_ncard_complproof · cited by 1