Generalized direct products
were introduced by B. H. Neuman and H. Neumann. In this paper we attempt to
study some properties of generalized direct decompositions of groups. In general,
decompositions of a given group into indecomposable generalized direct factors are
not unique up to isomorphisms. The main result of this paper is that if the
commutator subgroup of G is a cyclic p-group contained in the center Z(G) then any
two generalized direct decompositions of G into indecomposable generalized
direct factors with respect to its center Z(G) of G are isomorphic modulo
Z(G).
