Countable extensions of torsion Abelian groups

Peter Vassilev Danchev

On countable extensions of primary abelian groups

Peter Vassilev Danchev (2007)

Archivum Mathematicum

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It is proved that if $A$ is an abelian $p$ -group with a pure subgroup $G$ so that $A / G$ is at most countable and $G$ is either $p^{ω + n}$ -totally projective or $p^{ω + n}$ -summable, then $A$ is either $p^{ω + n}$ -totally projective or $p^{ω + n}$ -summable as well. Moreover, if in addition $G$ is nice in $A$ , then $G$ being either strongly $p^{ω + n}$ -totally projective or strongly $p^{ω + n}$ -summable implies that so is $A$ . This generalizes a classical result of Wallace (J. Algebra, 1971) for totally projective $p$ -groups as well as continues our recent investigations...

Notes on countable extensions of $p^{ω + n}$ -projectives

Peter Vassilev Danchev (2008)

Archivum Mathematicum

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We prove that if $G$ is an Abelian $p$ -group of length not exceeding $ω$ and $H$ is its $p^{ω + n}$ -projective subgroup for $n \in ℕ \cup {0}$ such that $G / H$ is countable, then $G$ is also $p^{ω + n}$ -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).

Displaying similar documents to “Countable extensions of torsion Abelian groups”

On countable extensions of primary abelian groups

Notes on countable extensions of p ω + n -projectives

Notes on countable extensions of $p^{ω + n}$ -projectives