Orthogonal projection and liftings of Hamilton-decomposable Cayley graphs on abelian groups

In this article we introduce the concept of (p,α)-switching trees and use it to provide sufficient conditions on the abelian groups G and H for when CAY (G×H;S∪B) is Hamilton-decomposable, given that CAY (G;S) is Hamilton-decomposable and B is a basis for H. Applications of this result to elementary abelian groups and Paley graphs are given.