The Schur multiplier of central product of groups

Let G be a central product of two groups H and K. We study second cohomology group of G, having coefficients in a divisible abelian group D with trivial G-action, in terms of the second cohomology groups of certain quotients of H and K. In particular, for D=C⁎, some of our results provide a refinement of results from Wiegold (1971) [10] and Eckmann et al. (1973) [2].