Symmetry group prerequisite for E-infinity in high energy physics

The work addresses the question of extending certain symplectic and exceptional Lie Symmetry groups to the realm of chaotic dynamics. Using a collection of simple examples, the technique of transfinite continuation is illustrated and various physically relevant results are obtained. The paper is intended as an elementary introduction to the use of symmetry groups in transfinite physics and as such is a sequel to a series of previous papers constituting the elementary and advanced mathematical prerequisite for a proper understanding of E-infinity theory.