Symmetry properties of autonomous integrating factors

Abstract:
We study the symmetry properties of integrating factors. The symmetries are delineated for the resulting integrals treated as equations and symmetries of the integrals as configurational invariants. The succession of terms (pattern) is noted. The general pattern for the solution symmetries for equations in the simplest form of maximal order is given. The question that arises is what happens when equations are in the normal form? We extend our discussions to include generalised and nonlocal symmetries.