| Title:
|
Pure subgroups (English) |
| Author:
|
Bican, Ladislav |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
126 |
| Issue:
|
3 |
| Year:
|
2001 |
| Pages:
|
649-652 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\lambda $ be an infinite cardinal. Set $\lambda _0=\lambda $, define $\lambda _{i+1}=2^{\lambda _i}$ for every $i=0,1,\dots $, take $\mu $ as the first cardinal with $\lambda _i<\mu $, $i=0,1,\dots $ and put $\kappa = (\mu ^{\aleph _0})^+$. If $F$ is a torsion-free group of cardinality at least $\kappa $ and $K$ is its subgroup such that $F/K$ is torsion and $|F/K|\le \lambda $, then $K$ contains a non-zero subgroup pure in $F$. This generalizes the result from a previous paper dealing with $F/K$ $p$-primary. (English) |
| Keyword:
|
torsion-free abelian groups |
| Keyword:
|
pure subgroup |
| Keyword:
|
$P$-pure subgroup |
| MSC:
|
20K20 |
| MSC:
|
20K27 |
| idZBL:
|
Zbl 0983.20054 |
| idMR:
|
MR1970267 |
| DOI:
|
10.21136/MB.2001.134196 |
| . |
| Date available:
|
2009-09-24T21:55:27Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134196 |
| . |
| Reference:
|
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| Reference:
|
[2] L. Bican: A note on pure subgroups.(to appear). Zbl 0969.20028, MR 1777650 |
| Reference:
|
[3] L. Bican, B. Torrecillas: On covers.(to appear). MR 1813494 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[6] L. Fuchs: Infinite Abelian Groups, vol. I and II.Academic Press, New York, 1973 and 1977. MR 0255673 |
| Reference:
|
[7] M. L. Teply: Torsion-free covers II.Israel J. Math. 23 (1976), 132–136. Zbl 0321.16014, MR 0417245 |
| Reference:
|
[8] J. Xu: Flat Covers of Modules.Lecture Notes in Mathematics 1634, Springer, Berlin, 1996. Zbl 0860.16002, MR 1438789 |
| . |
