Department of Mathematics,

Durban Institute of Technology,

PO Box 953, Steve Biko Campus,

Durban 4000,

SOUTH AFRICA

E-mail: moyos@nu.ac.za, moyos@dit.ac.za, leachp@nu.ac.za, leach@math.aegean.gr

**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.