Complete Symmetry Groups of Ordinary Differential Equations and Their Integrals: Some Basic Considerations

The concept of the complete symmetry group of a differential equation introduced by J.Krause (1994, J. Math. Phys. 35, 5734–5748) is extended to integrals of such equations.This paper is devoted to some aspects characterising complete symmetry groups.The algebras of the symmetries of both differential equations and integrals are studied in the context of equations for which the elements are represented by point or contact symmetries so that there is no ambiguity about the group.Both algebras and groups are found to be nonunique