{α : Type u_3} →
  {β : Type u_4} →
    [inst : Group α] →
      (a : α) →
        [inst_1 : MulAction α β] →
          (b : β) → ↑(MulAction.orbit (↥(Subgroup.zpowers a)) b) ≃ ZMod (Function.minimalPeriod (fun x => a • x) b)