×

*-pure subgroups of completely decomposable Abelian groups. (English) Zbl 0624.20037

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

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
PDFBibTeX XMLCite
Full Text: DOI