| Title:
|
On extensions of primary almost totally projective abelian groups (English) |
| Author:
|
Danchev, Peter V. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
133 |
| Issue:
|
2 |
| Year:
|
2008 |
| Pages:
|
149-155 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Suppose $G$ is a subgroup of the reduced abelian $p$-group $A$. The following two dual results are proved: $(*)$ If $A/G$ is countable and $G$ is an almost totally projective group, then $A$ is an almost totally projective group. $(**)$ If $G$ is countable and nice in $A$ such that $A/G$ is an almost totally projective group, then $A$ is an almost totally projective group. These results somewhat strengthen theorems due to Wallace (J. Algebra, 1971) and Hill (Comment. Math. Univ. Carol., 1995), respectively. (English) |
| Keyword:
|
totally projective group |
| Keyword:
|
almost totally projective group |
| Keyword:
|
countable group |
| Keyword:
|
extension |
| MSC:
|
20K10 |
| MSC:
|
20K25 |
| MSC:
|
20K27 |
| MSC:
|
20K35 |
| MSC:
|
20K40 |
| idZBL:
|
Zbl 1170.20310 |
| idMR:
|
MR2428310 |
| DOI:
|
10.21136/MB.2008.134056 |
| . |
| Date available:
|
2009-09-24T22:35:35Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134056 |
| . |
| Reference:
|
[1] P. V. Danchev: Generalized Dieudonné and Honda criteria.Alg. Colloq. 15 (2008). Zbl 1154.20043, MR 2418776 |
| Reference:
|
[2] P. V. Danchev: Generalized Dieudonné and Hill criteria.Portugal. Math. 65 (2008), 121–142. Zbl 1146.20034, MR 2387091 |
| Reference:
|
[3] P. V. Danchev, P. W. Keef: Generalized Wallace theorems.(to appear). MR 2498370 |
| Reference:
|
[4] P. V. Danchev, P. W. Keef: Dual Wallace theorems. Submitted.. |
| Reference:
|
[5] L. Fuchs: Infinite Abelian Groups, II.Mir, Moskva, 1977. (Russian) MR 0457533 |
| Reference:
|
[6] P. D. Hill: Almost coproducts of finite cyclic groups.Commentat. Math. Univ. Carolin. 36 (1995), 795–804. Zbl 0845.20038, MR 1378700 |
| Reference:
|
[7] P. D. Hill, W. D. Ullery: Almost totally projective groups.Czech. Math. J. 46 (1996), 249–258. MR 1388614 |
| Reference:
|
[8] P. D. Hill, W. D. Ullery: Isotype separable subgroups of totally projective groups.Proc. Padova Conf. 1994, Abelian Groups and Modules, A. Facchini (ed.), Kluwer Acad. Publ., Dordrecht, 1995, pp. 291–300. MR 1378207 |
| Reference:
|
[9] K. D. Wallace: On mixed groups of torsion-free rank one with totally projective primary components.J. Algebra 17 (1971), 482–488. Zbl 0215.39902, MR 0272891, 10.1016/0021-8693(71)90005-6 |
| . |
