ABELIAN TORSION GROUPS WITH A PSEUDOCOMPACT GROUP TOPOLOGY

Two questions are posed: (a) Which Abelian torsion groups admit a PGT (pseudocompact group topology)? (b) If an Abelian torsion group G admits a PGT. for which cardinal numbers alpha may such a topology F be chosen SO that the weight of the space [G. F] is equal to alpha? The authors answer question (a) completely (Theorems 3.17 and 3.19). In Theorem 3.24 for alpha greater-than-or-equal-to gamma greater-than-or-equal-to omega they characterize those Abelian torsion groups of cardinality gamma which admit a PGT of weight alpha. This furnishes partial answers to (h).