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 a may such a topology F be chosen so that the weight of the space > G,F > is equal to a? The authors answer question (a) completely (Theorems 3.17 and 3.19). In Theorem 3.24 for α > γ > ω they characterize those Abelian torsion groups of cardinality y which admit a PGT of weight a. This furnishes partial answers to (b)
