λλ-symmetries of some chains of ordinary differential equations

We introduce a new local transformation that connects certain hierarchies of ODEs with the Riccati chain. Such transformation is derived from the existence of a common λλ-symmetry for all the equations of any of the studied chains. We provide a unified procedure to derive the solutions of all the equations of a given chain in terms of the solutions of the higher Riccati equations. The higher Abel equations are solved by applying this method. Some features on Jacobi last multipliers and nonlocal symmetries for some specific chains are also established.