Geodesic
Notes on countable extensions of $p^{\omega +n}$-projectives
Archivum mathematicum, Tome 44 (2008) no. 1, pp. 37-40.

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We prove that if $G$ is an Abelian $p$-group of length not exceeding $\omega $ and $H$ is its $p^{\omega +n}$-projective subgroup for $n\in {\mathbb{N}} \cup \lbrace 0\rbrace $ such that $G/H$ is countable, then $G$ is also $p^{\omega +n}$-projective. This enlarges results of ours in (Arch. Math. (Brno), 2005, 2006 and 2007) as well as a classical result due to Wallace (J. Algebra, 1971).
Classification : 20K10, 20K25, 20K27, 20K35, 20K40
Keywords: abelian groups; countable factor-groups; $p^{\omega +n}$-projective groups 
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     author = {Danchev, Peter},
     title = {Notes on countable extensions of~$p^{\omega +n}$-projectives},
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Danchev, Peter. Notes on countable extensions of $p^{\omega +n}$-projectives. Archivum mathematicum, Tome 44 (2008) no. 1, pp. 37-40. http://geodesic.mathdoc.fr/item/ARM_2008__44_1_a4/