We calculate the three-loop gauge p-function for an abelian N = 1 supe
rsymmetric gauge theory, using DRED. We construct a coupling constant
redefinition that relates the result to the corresponding term in the
NSVZ beta-function, and by generalising this redefinition to the non-a
belian case we derive the DRED three-loop gauge beta-function for the
non-abelian case.