Theorems · Theorem · group theory

MulAction.isPreprimitive_stabilizer_subgroup

∀ {M : Type u_1} {α : Type u_2} [inst : Group M] [inst_1 : MulAction M α] {s : Set α}
  [MulAction.IsPreprimitive ↥(MulAction.stabilizer M s) ↑s] {G : Subgroup M},
  MulAction.stabilizer M s ≤ G → MulAction.IsPreprimitive ↥(MulAction.stabilizer (↥G) s) ↑s

A (mostly trivial) primitivity criterion for stabilizers.

Defined in: Mathlib.GroupTheory.Perm.MaximalSubgroups
Cited by: 1 results in Mathlib
Foundations: Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Group MulAction MulAction.IsPreprimitive

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Cites11

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
Set.Elemstatement and proof · cited by 7,166
Groupstatement and proof · cited by 6,238
Subgroupstatement and proof · cited by 3,593
MulActionstatement and proof · cited by 1,294
Subtype.propproof · cited by 505
MulAction.stabilizerstatement and proof · cited by 254
MulActionHomproof · cited by 124
Set.mulActionSetstatement · cited by 95
MulAction.IsPreprimitivestatement and proof · cited by 50
MulAction.IsPreprimitive.of_surjectiveproof · cited by 8

Cited by1

Results whose statement or proof uses this declaration.

Equiv.Perm.isCoatom_stabilizer_of_ncard_lt_ncard_complproof · cited by 1