ESSENTIALLY RIGID FLOPPY SUBGROUPS OF THE BAER-SPECKER GROUP

We construct a pure subgroup G of the Baer-Specker group Z(omega) with a ''small'' endomorphism ring giving a split realization of Z, in the sense that End G = Z + Fin G with I Fin G I less than or equal to 2(N o), where Fin G denotes the ideal of all endomorphisms of G of finite rank, while its dual G = Hom(G, Z) is as large as possible, i.e. of c ardinal 2(No). Our group G gives a complete answer to a question of Ir win (1993). Note that a recent paper [3] answered Irwin's question und er the assumption of the continuum hypothesis CH.