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Keywords:
torsion-free abelian groups; Butler groups; $B_2$-groups; $\aleph _0$-prebalanced subgroups; completely decomposable groups; separative subgroups
torsion-free abelian groups; Butler groups; $B_2$-groups; $\aleph _0$-prebalanced subgroups; completely decomposable groups; separative subgroups
Summary:
It is shown, under ZFC, that a $B_2$-group has the interesting property of being $\aleph _0$-prebalanced in every torsion-free abelian group in which it is a pure subgroup. As a consequence, we obtain alternate proofs of some well-known theorems on $B_2$-groups.
References:
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[F-1] Fuchs L.: Infinite Abelian Groups, vol. 2. Academic Press, New York, 1973. MR 0349869
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[R] Rangaswamy K.M.: A homological characterization of abelian $B_2$-groups. Proc. Amer. Math. Soc., to appear. MR 1186993
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