  This paper investigates the d = 4, N = 4 Abelian, global Super-Yang Mills
system (SUSY-YM). It is shown how the N = 2 Fayet Hypermultiplet (FH) and N = 2
vector multiplet (VM) are embedded within. The central charges provide a
plethora of information as to further symmetries of the Lagrangian. Several of
these symmetries are calculated to second order. It is hoped that
investigations such as these may yield avenues to help solve the auxiliary
field closure problem for d = 4, N = 4, SUSY-YM and the d = 4, N = 2
Fayet-Hypermultiplet, without using an infinite number of auxiliary fields.
