In order to apply known general theorems about the effective propertie
s of recursive structures in a particular recursive structure, it is n
ecessary to verify that certain decidability conditions are satisfied.
This requires the determination of when certain relations, called bac
k and forth relations, hold between finite strings of elements from th
e structure. Here we determine this for recursive reduced abelian p-gr
oups, thus enabling us to apply these theorems.