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Butler group; generalized regular subgroup
A torsionfree abelian group $B$ is called a Butler group if $Bext(B,T) = 0$ for any torsion group $T$. It has been shown in [DHR] that under $CH$ any countable pure subgroup of a Butler group of cardinality not exceeding $\aleph_\omega$ is again Butler. The purpose of this note is to show that this property has any Butler group which can be expressed as a smooth union $\cup_{\alpha < \mu}B_\alpha$ of pure subgroups $B_\alpha$ having countable typesets.
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