| Title:
|
Notes on countable extensions of $p^{\omega +n}$-projectives (English) |
| Author:
|
Danchev, Peter |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
44 |
| Issue:
|
1 |
| Year:
|
2008 |
| Pages:
|
37-40 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that if $G$ is an Abelian $p$-group of length not exceeding $\omega $ and $H$ is its $p^{\omega +n}$-projective subgroup for $n\in {\mathbb{N}} \cup \lbrace 0\rbrace $ such that $G/H$ is countable, then $G$ is also $p^{\omega +n}$-projective. This enlarges results of ours in (Arch. Math. (Brno), 2005, 2006 and 2007) as well as a classical result due to Wallace (J. Algebra, 1971). (English) |
| Keyword:
|
abelian groups |
| Keyword:
|
countable factor-groups |
| Keyword:
|
$p^{\omega +n}$-projective groups |
| MSC:
|
20K10 |
| MSC:
|
20K25 |
| MSC:
|
20K27 |
| MSC:
|
20K35 |
| MSC:
|
20K40 |
| idZBL:
|
Zbl 1203.20046 |
| idMR:
|
MR2431229 |
| . |
| Date available:
|
2008-06-06T22:52:40Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/108094 |
| . |
| Reference:
|
[1] Danchev, P.: Countable extensions of torsion abelian groups.Arch. Math. (Brno) 41 (3) (2005), 265–272. Zbl 1114.20030, MR 2188382 |
| Reference:
|
[2] Danchev, P.: Generalized Dieudonné criterion.Acta Math. Univ. Comenian. 74 (1) (2005), 15–26. Zbl 1111.20045, MR 2154393 |
| Reference:
|
[3] Danchev, P.: A note on the countable extensions of separable $p^{\omega +n}$-projective abelian $p$-groups.Arch. Math. (Brno) 42 (3) (2006), 251–254. Zbl 1152.20045, MR 2260384 |
| Reference:
|
[4] Danchev, P.: On countable extensions of primary abelian groups.Arch. Math. (Brno) 43 (1) (2007), 61–66. Zbl 1156.20044, MR 2310125 |
| Reference:
|
[5] Danchev, P., Keef, P.: Generalized Wallace theorems.Math. Scand. (to appear). MR 2498370 |
| Reference:
|
[6] Dieudonné, J.: Sur les $p$-groupes abeliens infinis.Portugal. Math. 11 (1) (1952), 1–5. MR 0046356 |
| Reference:
|
[7] Fuchs, L.: Infinite Abelian Groups, I, II.Mir, Moskva, 1974 and 1977, (in Russian). MR 0457533 |
| Reference:
|
[8] Fuchs, L.: Subfree valued vector spaces.Lecture Notes in Math. 616 (1977), 158–167. Zbl 0389.15001, MR 0480700, 10.1007/BFb0068194 |
| Reference:
|
[9] Hill, P., Megibben, C.: Extensions of torsion-complete groups.Proc. Amer. Math. Soc. 44 (2) (1974), 259–262. Zbl 0292.20050, MR 0340452, 10.1090/S0002-9939-1974-0340452-3 |
| Reference:
|
[10] Nunke, R.: Topics in Abelian Groups.ch. Purity and subfunctors of the identity, pp. 121–171, Scott, Foresman and Co., Chicago, 1963. MR 0169913 |
| Reference:
|
[11] Nunke, R.: Homology and direct sums of countable abelian groups.Math. Z. 101 (3) (1967), 182–212. Zbl 0173.02401, MR 0218452, 10.1007/BF01135839 |
| Reference:
|
[12] Wallace, K.: On mixed groups of torsion-free rank one with totally projective primary components.J. Algebra 17 (4) (1971), 482–488. Zbl 0215.39902, MR 0272891, 10.1016/0021-8693(71)90005-6 |
| . |
