ABSTRACT
Necessary and sufficient conditions for the existence of functions f 1 , f 2 : G → H https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315139975/1413b990-0cd9-4945-9840-4ee4de0fda23/content/eq37.tif"/>
between the Abelian groups G and H, H non–trivial, with prescribed group of periods, that sum to a function f 1 + f 2: G → H with prescribed group of periods are given.
In the case that H has an element of order greater than two these conditions are given in terms of conditions on the subgroup lattice of G and the existence of a particular subgroup of H. In the case that every element of H is of order two, but H ≇ ℤ2, additional arithmetic conditions, which are required, are given. The case where H ≅ Z 2 requires separate treatment.
