alternatingGroup_le_of_isPreprimitive_of_isCycle_mem

English

Conjugation by an element maps fixingSubgroup to fixingSubgroup under corresponding conjugation.

Русский

Уголовление подгруппы фиксации сохраняется под соответствующим сопряжением.

LaTeX

$$IsPreprimitive (fixingSubgroup G s) (ofFixingSubgroup G s) ≃ IsPreprimitive (fixingSubgroup G (g•s)) (ofFixingSubgroup G (g•s))$$

Lean4

/-- A primitive subgroup of `Equiv.Perm α` that contains a cycle of prime order
contains the alternating group. -/
axiom alternatingGroup_le_of_isPreprimitive_of_isCycle_mem (hG : IsPreprimitive G α) {p : ℕ} (hp : p.Prime)
    (hp' : p + 3 ≤ Nat.card α) {g : Perm α} (hgc : g.IsCycle) (hgp : g.support.card = p) (hg : g ∈ G) :
    alternatingGroup α ≤ G

Похожие утверждения