Theorems · Theorem · group theory

Set.powersetCard.isPreprimitive_alternatingGroup

∀ {α : Type u_2} [inst : DecidableEq α] [inst_1 : Fintype α] {n : ℕ},
  3 ≤ n → n < Nat.card α → Nat.card α ≠ 2 * n → MulAction.IsPreprimitive ↥(alternatingGroup α) ↑(Set.powersetCard α n)

The action of alternatingGroup α on Set.powersetCard α n is preprimitive provided 1 ≤ n < Nat.card α and Nat.card α ≠ 2 * n.

Defined in

Mathlib.GroupTheory.GroupAction.SubMulAction.Combination

Cited by

2 results in Mathlib

Foundations

Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqFintype