On p-local Abelian groups with decomposition bases (Q1109145)

A study is presented of those p-local abelian groups G which possess a nice decomposition basis with cokernel an S-group, and we use the theory of cotorsion groups and techniques which were successful in characterizing the structure of summands of S-groups to prove that such a group must decompose into a direct sum of a Warfield group and an S- group. From this characterization of these groups, we are able to show that a summand of a direct sum of a Warfield group and an S-group is itself a direct sum of a Warfield group and an S-group, and this extends the structure theory of Warfield groups and of S-groups to this larger class of groups. Finally, another application of the main result is given which describes this class of groups as those isotype subgroups of p- local Warfield groups with cokernel a coproduct of countable torsion groups under the coset valuation.