Geodesic
A note on the countable extensions of separable $p\sp {\omega+n}$-projective abelian $p$-groups
Archivum mathematicum, Tome 42 (2006) no. 3, pp. 251-254.

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It is proved that if $G$ is a pure $p^{\omega + n}$-projective subgroup of the separable abelian $p$-group $A$ for $n\in {N}\cup \lbrace 0\rbrace $ such that $|A/G|\le \aleph _0$, then $A$ is $p^{\omega +n}$-projective as well. This generalizes results due to Irwin-Snabb-Cutler (CommentṀathU̇nivṠtṖauli, 1986) and the author (Arch. Math. (Brno), 2005).
Classification : 20K10
Keywords: countable extensions; separable groups; $p^{\omega +n}$-projective groups 
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     title = {A note on the countable extensions of separable $p\sp {\omega+n}$-projective abelian $p$-groups},
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Danchev, Peter. A note on the countable extensions of separable $p\sp {\omega+n}$-projective abelian $p$-groups. Archivum mathematicum, Tome 42 (2006) no. 3, pp. 251-254. http://geodesic.mathdoc.fr/item/ARM_2006__42_3_a6/