| Title:
|
Countable extensions of torsion Abelian groups (English) |
| Author:
|
Danchev, Peter |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
41 |
| Issue:
|
3 |
| Year:
|
2005 |
| Pages:
|
265-272 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Suppose $A$ is an abelian torsion group with a subgroup $G$ such that $A/G$ is countable that is, in other words, $A$ is a torsion countable abelian extension of $G$. A problem of some group-theoretic interest is that of whether $G \in \mathbb K$, a class of abelian groups, does imply that $A\in \mathbb K$. The aim of the present paper is to settle the question for certain kinds of groups, thus extending a classical result due to Wallace (J. Algebra, 1981) proved when $\mathbb K$ coincides with the class of all totally projective $p$-groups. (English) |
| Keyword:
|
countable factor-groups |
| Keyword:
|
$\Sigma $-groups |
| Keyword:
|
$\sigma $-summable groups |
| Keyword:
|
summable groups |
| Keyword:
|
$p^{\omega + n}$-projective groups |
| MSC:
|
20K10 |
| MSC:
|
20K35 |
| idZBL:
|
Zbl 1114.20030 |
| idMR:
|
MR2188382 |
| . |
| Date available:
|
2008-06-06T22:46:10Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107957 |
| . |
| Reference:
|
[1] Danchev P. V.: Commutative group algebras of $\sigma $-summable abelian groups.Proc. Amer. Math. Soc. (9) 125 (1997), 2559–2564. Zbl 0886.16024, MR 1415581 |
| Reference:
|
[2] Danchev P. V.: Commutative group algebras of abelian $\Sigma $-groups.Math. J. Okayama Univ. 40 (1998), 77–90. MR 1755921 |
| Reference:
|
[3] Danchev P. V.: Commutative group algebras of highly torsion-complete abelian $p$-groups.Comment. Math. Univ. Carolin. (4) 44 (2003), 587–592. Zbl 1101.20001, MR 2062875 |
| Reference:
|
[4] Danchev P. V.: Commutative group algebras of summable abelian $p$-groups.Comm. Algebra, in press. |
| Reference:
|
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| Reference:
|
[6] Fuchs L.: Infinite Abelian Groups.Volumes I and II, Mir, Moskva, 1974 and 1977. (In Russian.) Zbl 0338.20063, MR 0457533 |
| Reference:
|
[7] Hill P. D.: Criteria for freeness in groups and valuated vector spaces.Lect. Notes in Math. 616 (1977), 140–157. Zbl 0372.20041, MR 0486206 |
| Reference:
|
[8] Hill P. D., Megibben C. K.: On direct sums of countable groups and generalizations.Études sur les Groupes Abéliens, Paris (1968), 183–206. Zbl 0203.32705, MR 0242943 |
| 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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| . |
