ALMOST TOTALLY INJECTIVE p-GROUPS

Abstract

Abelian p-groups A are studied which are almost totally injective in the sense that pσExt(ZZ (pm∞), A/pσA) = 0 for every ordinal σ. It is shown that these are exactly those p-groups in whose cotorsion hulls the Ulm factors have torsion basic subgroups. They can also be characterized as summands in every p-group in which they are isotype with divisible quotients. An embedding theorem in these groups is also established. (MOS subject classification: 20 K 10).