| Title:
|
On a class of locally Butler groups (English) |
| Author:
|
Bican, Ladislav |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
4 |
| Year:
|
1991 |
| Pages:
|
597-600 |
| . |
| Category:
|
math |
| . |
| Summary:
|
A torsionfree abelian group $B$ is called a Butler group if $Bext(B,T) = 0$ for any torsion group $T$. It has been shown in [DHR] that under $CH$ any countable pure subgroup of a Butler group of cardinality not exceeding $\aleph_\omega$ is again Butler. The purpose of this note is to show that this property has any Butler group which can be expressed as a smooth union $\cup_{\alpha < \mu}B_\alpha$ of pure subgroups $B_\alpha$ having countable typesets. (English) |
| Keyword:
|
Butler group |
| Keyword:
|
generalized regular subgroup |
| MSC:
|
20K20 |
| MSC:
|
20K27 |
| MSC:
|
20K35 |
| idZBL:
|
Zbl 0748.20029 |
| idMR:
|
MR1159805 |
| . |
| Date available:
|
2009-01-08T17:47:19Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118438 |
| . |
| Reference:
|
[A] Arnold D.: Notes on Butler groups and balanced extensions.Boll. Un. Mat. Ital. A(6) 5 (1986), 175-184. Zbl 0601.20050, MR 0850285 |
| Reference:
|
[B1] Bican L.: Splitting in abelian groups.Czech. Math. J. 28 (1978), 356-364. Zbl 0421.20022, MR 0480778 |
| Reference:
|
[B2] Bican L.: Purely finitely generated groups.Comment. Math. Univ. Carolinae 21 (1980), 209-218. MR 0580678 |
| Reference:
|
[BS] Bican L., Salce L., HASH(0x91ad320): Infinite rank Butler groups.Proc. Abelian Group Theory Conference, Honolulu, Lecture Notes in Math., vol. 1006, Springer-Verlag, 1983, 171-189. |
| Reference:
|
[BSS] Bican L., Salce L., Štěpán J.: A characterization of countable Butler groups.Rend. Sem. Mat. Univ. Padova 74 (1985), 51-58. MR 0818715 |
| Reference:
|
[B] Butler M.C.R.: A class of torsion-free abelian groups of finite rank.Proc. London Math. Soc. 15 (1965), 680-698. Zbl 0131.02501, MR 0218446 |
| Reference:
|
[D] Dugas M.: On some subgroups of infinite rank Butler groups.Rend. Sem. Mat. Univ. Padova 79 (1988), 153-161. Zbl 0667.20043, MR 0964027 |
| Reference:
|
[DHR] Dugas M., Hill P., Rangaswamy K.M.: Infinite rank Butler groups II.Trans. Amer. Math. Soc. 320 (1990), 643-664. MR 0963246 |
| Reference:
|
[DR] Dugas M., Rangaswamy K.M.: Infinite rank Butler groups,.Trans. Amer. Math. Soc. 305 (1988), 129-142. Zbl 0641.20036, MR 0920150 |
| Reference:
|
[F1] Fuchs L.: Infinite Abelian groups.vol. I and II, Academic Press, New York, 1973 and 1977. Zbl 0338.20063, MR 0255673 |
| Reference:
|
[F2] Fuchs L.: Infinite rank Butler groups.preprint. |
| Reference:
|
[FM] Fuchs L., Metelli C.: Countable Butler groups.Contemporary Math., to appear. Zbl 0769.20025, MR 1176115 |
| Reference:
|
[FV] Fuchs L., Viljoen G.: Note on the extensions of Butler groups.Bull. Austral. Math. Soc. 41 (1990), 117-122. MR 1043972 |
| . |
