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Keywords:
abelian groups; countable factor-groups; $p^{\omega +n}$-projective groups
abelian groups; countable factor-groups; $p^{\omega +n}$-projective groups
Summary:
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).
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