A note on the countable extensions of separable $p^{\omega +n}$-projective abelian $p$-groups

P. Danchev

13, General Kutuzov Street, block 7, floor 2, flat 4, 4003 Plovdiv, Bulgaria

E-mail. pvdanchev@yahoo.com

It is proved that if $G$ is a pure $p^{\omega + n}$-projective subgroup of the separable abelian

$p$-group $A$ for $n\in {\Bbb N}\cup \{0\}$ such that $|A/G|\leq \aleph_0$, then $A$ is $p^{\omega+n}$-projective as well. This generalizes results due to Irwin-Snabb-Cutler (Comment\. Math\. Univ\. St\. Pauli,

1986) and the author (Arch.\ Math.\ (Brno), 2005).

AMSclassification. 20K10.

Keywords.   Countable extensions, separable groups, $p^{\omega+n}$-projective groups.