Factorisation of semiregular relative difference sets

Pott has shown that the product of two semiregular relative difference sets in commuting groups El and E2 relative to their intersection subgroup C is itself a semiregular relative difference set in their amalgamated direct product. We generalise this result in the case that C is central in El and in E2 by using an equivalence with corresponding co cycles 7./Jl and 'l/J2' We prove that in the central case the converse of this product construction holds: if there is a relative difference set in the central extension corresponding to 'l/Jl ® 'l/J2 it factorises as a product of relative difference sets in El and E2•