Algebraic structures of generalised symmetries of n th-order scalar ordinary differential equations of maximal lie point symmetry

We compute for the representative scalar ordinary differential equation of maximal point symmetry the generalised symmetries of order-one and two. We examine the Lie Brackets for the generalised symmetries and see that closure does not occur for generalised symmetries of order-two. Consequently all generalised symmetries up to the maximum order possible must be admitted.