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Keywords:
countable extensions; separable groups; $p^{\omega +n}$-projective groups
countable extensions; separable groups; $p^{\omega +n}$-projective groups
Summary:
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).
References:
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[2] Irwin, J., Snabb, T. and Cutler, D.: On $p^{\omega +n}$-projective $p$-groups. Comment. Math. Univ. St. Pauli 35(1) (1986), 49–52. MR 0838187
[3] Nunke, R.: Purity and subfunctors of the identity. Topics in Abelian Groups, Scott, Foresman and Co., 1963, 121–171. MR 0169913
[4] Nunke, R.: Homology and direct sums of countable abelian groups. Math. Z. 101(3) (1967), 182–212. MR 0218452 | Zbl 0173.02401
[5] Wallace, K.: On mixed groups of torsion-free rank one with totally projective primary components. J. Algebra 17(4) (1971), 482–488. MR 0272891 | Zbl 0215.39902
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