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$ *$-pure subgroups of completely decomposable abelian groups

Author: Loyiso G. Nongxa
Journal: Proc. Amer. Math. Soc. 100 (1987), 613-618
MSC: Primary 20K27; Secondary 20K15, 20K20
MathSciNet review: 894425
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Abstract: In this note we prove that

(i) homogeneous $ *$-pure subgroups of completely decomposable groups are completely decomposable,

(ii) $ *$-pure subgroups of finite rank completely decomposable groups are almost completely decomposable.

We also characterize those reduced completely decomposable groups $ G$, with $ T(G)$ satisfying the maximum condition, any $ *$-pure subgroup of which is also completely decomposable.

References [Enhancements On Off] (What's this?)

  • [1] Ladislav Bican, Completely decomposable abelian groups any pure subgroup of which is completely decomposable, Czechoslovak Math. J. 24(99) (1974), 176–191. MR 0348009
  • [2] H. Bowman and K. M. Rangaswamy, On special balanced subgroups of torsion-free abelian groups, preprint.
  • [3] László Fuchs, Infinite abelian groups. Vol. II, Academic Press, New York-London, 1973. Pure and Applied Mathematics. Vol. 36-II. MR 0349869
  • [4] Loyiso G. Nongxa, Homogeneous subgroups of completely decomposable groups, Arch. Math. (Basel) 42 (1984), no. 3, 208–213. MR 751497, 10.1007/BF01191177

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Article copyright: © Copyright 1987 American Mathematical Society