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Title: On countable extensions of primary abelian groups (English)
Author: Danchev, P. V.
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 43
Issue: 1
Year: 2007
Pages: 61-66
Summary lang: English
Category: math
Summary: 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 $p^{\omega +n}$-totally projective or $p^{\omega +n}$-summable, then $A$ is either $p^{\omega +n}$-totally projective or $p^{\omega +n}$-summable as well. Moreover, if in addition $G$ is nice in $A$, then $G$ being either strongly $p^{\omega +n}$-totally projective or strongly $p^{\omega +n}$-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 in (Arch. Math. (Brno), 2005 and 2006). Some other related results are also established. (English)
Keyword: countable quotient groups
Keyword: $\omega $-elongations
Keyword: $p^{\omega +n}$-totally projective groups
Keyword: $p^{\omega +n}$-summable groups
MSC: 20K10
MSC: 20K15
idZBL: Zbl 1156.20044
idMR: MR2310125
Date available: 2008-06-06T22:50:32Z
Last updated: 2012-05-10
Stable URL:
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