Nongxa, Loyiso G. *-pure subgroups of completely decomposable Abelian groups. (English) Zbl 0624.20037 Proc. Am. Math. Soc. 100, 613-618 (1987). A subgroup H of a torsionfree group G is said to be *-pure if it is pure and \(<H^*(\tau)>_*=H\cap <G^*(\tau)>_*\) for every type \(\tau\). Homogeneous *-pure subgroups of completely decomposable groups are completely decomposable (Theorem 1), *-pure subgroups of finite rank completely decomposable groups are almost completely decomposable (Theorem 2). A characterization of the class of reduced completely decomposable groups every *-pure subgroup of which is completely decomposable is presented (Theorem 4). Reviewer: L.Bican Cited in 3 Documents MSC: 20K20 Torsion-free groups, infinite rank 20K25 Direct sums, direct products, etc. for abelian groups 20K27 Subgroups of abelian groups 20K15 Torsion-free groups, finite rank Keywords:torsionfree group; type; *-pure subgroups; completely decomposable groups PDFBibTeX XMLCite \textit{L. G. Nongxa}, Proc. Am. Math. Soc. 100, 613--618 (1987; Zbl 0624.20037) Full Text: DOI