Theorems · Theorem · group theory

MulAction.IwasawaStructure.isSimpleGroup

∀ {M : Type u_1} [inst : Group M] {α : Type u_2} [inst_1 : MulAction M α] [Nontrivial M],
  commutator M = ⊤ →
    ∀ [MulAction.IsQuasiPreprimitive M α] (IwaS : MulAction.IwasawaStructure M α), FaithfulSMul M α → IsSimpleGroup M

The Iwasawa criterion for simplicity

Defined in: Mathlib.GroupTheory.GroupAction.Iwasawa
Cited by: 1 results in Mathlib
Foundations: Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Group MulAction Nontrivial MulAction.IsQuasiPreprimitive

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Cites21

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

Top.topstatement and proof · cited by 9,680
Groupstatement and proof · cited by 6,238
Set.univproof · cited by 3,945
Subgroupstatement and proof · cited by 3,593
Nontrivialstatement and proof · cited by 2,416
one_smulproof · cited by 1,374
MulActionstatement and proof · cited by 1,294
le_transproof · cited by 985
FaithfulSMulstatement and proof · cited by 340
Subgroup.Normalproof · cited by 334
top_le_iffproof · cited by 175
Set.eq_univ_iff_forallproof · cited by 93

Cited by1

Results whose statement or proof uses this declaration.

Matrix.ProjectiveSpecialLinearGroup.rank_two_simple'proof · cited by 1