The balanced-projective dimension of p-local Abelian groups (Q1090420)

The author extends the Fuchs-Hill theorem on the balanced projective dimension of abelian p-groups to arbitrary p-local abelian groups. The approach and the results are similar to those of \textit{L. Fuchs} and \textit{P. Hill} [Trans. Am. Math. Soc. 293, 99-112 (1986; Zbl 0602.20047)]. The techniques developed by Paul Hill in his earlier study of isotype subgroups of totally projective p-groups are put into good use. An interesting consequence is that any p-local Warfield group and also any countable p-local group must have balanced projective dimension \(\leq 1\).