Ladislav Bican, KA MFF UK, Sokolovska 83, 186 75 Praha 8, Czech Republic, e-mail: bican@karlin.mff.cuni.cz
Abstract: Let $\lambda$ be an infinite cardinal. Set $\lambda_0=\lambda$, define $\lambda_{i+1}=2^{\lambda_i}$ for every $i=0,1,\dots$, take $\mu$ as the first cardinal with $\lambda_i<\mu$, $i=0,1,\dots$ and put $\kappa= (\mu^{\aleph_0})^+$. If $F$ is a torsion-free group of cardinality at least $\kappa$ and $K$ is its subgroup such that $F/K$ is torsion and $|F/K|\leq\lambda$, then $K$ contains a non-zero subgroup pure in $F$. This generalizes the result from a previous paper dealing with $F/K$ $p$-primary.
Keywords: torsion-free abelian groups, pure subgroup, $P$-pure subgroup
Classification (MSC 2000): 20K20
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