| 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:
|
http://hdl.handle.net/10338.dmlcz/108050 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Danchev P.: Characteristic properties of large subgroups in primary abelian groups.Proc. Indian Acad. Sci. Math. Sci. 104 (3) (2004), 225–233. Zbl 1062.20059, MR 2083463 |
| Reference:
|
[4] Danchev P.: Countable extensions of torsion abelian groups.Arch. Math. (Brno) 41 (3) (2005), 265–272. Zbl 1114.20030, MR 2188382 |
| Reference:
|
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| Reference:
|
[6] Danchev P.: Generalized Wallace theorems.submitted. Zbl 1169.20029 |
| Reference:
|
[7] Danchev P.: Theorems of the type of Cutler for abelian $p$-groups.submitted. Zbl 1179.20046 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| . |
