Theorems · Theorem · group theory

MulAction.isPreprimitive_fixingSubgroup_insert_iff

∀ {G : Type u_1} [inst : Group G] {α : Type u_2} [inst_1 : MulAction G α] {a : α}
  {t : Set ↥(SubMulAction.ofStabilizer G a)},
  MulAction.IsPreprimitive ↥(fixingSubgroup G (insert a (Subtype.val '' t)))
      ↥(SubMulAction.ofFixingSubgroup G (insert a (Subtype.val '' t))) ↔
    MulAction.IsPreprimitive ↥(fixingSubgroup (↥(MulAction.stabilizer G a)) t)
      ↥(SubMulAction.ofFixingSubgroup (↥(MulAction.stabilizer G a)) t)

Defined in

Mathlib.GroupTheory.GroupAction.MultiplePrimitivity

Cited by

1 results in Mathlib

Foundations

Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupMulAction