| Title:
|
A property of $B_2$-groups (English) |
| Author:
|
Rangaswamy, K. M. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
35 |
| Issue:
|
4 |
| Year:
|
1994 |
| Pages:
|
627-631 |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is shown, under ZFC, that a $B_2$-group has the interesting property of being $\aleph _0$-prebalanced in every torsion-free abelian group in which it is a pure subgroup. As a consequence, we obtain alternate proofs of some well-known theorems on $B_2$-groups. (English) |
| Keyword:
|
torsion-free abelian groups |
| Keyword:
|
Butler groups |
| Keyword:
|
$B_2$-groups |
| Keyword:
|
$\aleph _0$-prebalanced subgroups |
| Keyword:
|
completely decomposable groups |
| Keyword:
|
separative subgroups |
| MSC:
|
20K20 |
| MSC:
|
20K25 |
| MSC:
|
20K27 |
| idZBL:
|
Zbl 0823.20058 |
| idMR:
|
MR1321233 |
| . |
| Date available:
|
2009-01-08T18:13:53Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118704 |
| . |
| Reference:
|
[AH] Albrecht U., Hill P.: Butler groups of infinite rank and Axiom-3.Czech. Math. J. 37 (1987), 293-309. Zbl 0628.20045, MR 0882600 |
| Reference:
|
[BF] Bican L., Fuchs L.: Subgroups of Butler groups.to appear. Zbl 0802.20045, MR 1378188 |
| Reference:
|
[DHR] Dugas M., Hill P., Rangaswamy K.M.: Butler groups of infinite rank.Trans. Amer. Math. Soc. 320 (1990), 643-664. Zbl 0708.20018, MR 0963246 |
| Reference:
|
[F-1] Fuchs L.: Infinite Abelian Groups, vol. 2.Academic Press, New York, 1973. MR 0349869 |
| Reference:
|
[F-2] Fuchs L.: Butler Groups of Infinite Rank.to appear. Zbl 0842.20045, MR 1316995 |
| Reference:
|
[HM] Hill P., Megibben C.: Pure subgroups of torsion-free groups.Trans. Amer. Math. Soc. 303 (1987), 765-778. Zbl 0627.20028, MR 0902797 |
| Reference:
|
[R] Rangaswamy K.M.: A homological characterization of abelian $B_2$-groups.Proc. Amer. Math. Soc., to appear. MR 1186993 |
| . |
