| Title:
|
On extensions of bounded subgroups in Abelian groups (English) |
| Author:
|
Gabriyelyan, S. S. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
55 |
| Issue:
|
2 |
| Year:
|
2014 |
| Pages:
|
175-188 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is well-known that every bounded Abelian group is a direct sum of finite cyclic subgroups. We characterize those non-trivial bounded subgroups $H$ of an infinite Abelian group $G$, for which there is an infinite subgroup $G_0$ of $G$ containing $H$ such that $G_0$ has a special decomposition into a direct sum which takes into account the properties of $G$, and which induces a natural decomposition of $H$ into a direct sum of finite subgroups. (English) |
| Keyword:
|
Abelian group |
| Keyword:
|
bounded group |
| Keyword:
|
simple extension |
| MSC:
|
20K21 |
| MSC:
|
20K27 |
| idZBL:
|
Zbl 06391535 |
| idMR:
|
MR3193923 |
| . |
| Date available:
|
2014-06-07T15:32:15Z |
| Last updated:
|
2016-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143799 |
| . |
| Reference:
|
[1] Fuchs L.: Abelian Groups.Budapest: Publishing House of the Hungarian Academy of Sciences 1958, Pergamon Press, London, third edition, reprinted 1967. Zbl 1265.06054, MR 0106942 |
| Reference:
|
[2] Gabriyelyan S.S.: Finitely generated subgroups as a von Neumann radical of an Abelian group.Mat. Stud. 38 (2012), 124–138. MR 3057998 |
| Reference:
|
[3] Gabriyelyan S.S.: Bounded subgroups as a von Neumann radical of an Abelian group.preprint. |
| Reference:
|
[4] Markov A.A.: On free topological groups.Izv. Akad. Nauk SSSR Ser. Mat. 9 (1945), 3–64 (in Russian); English transl. in: Amer. Math. Soc. Transl. (1) 8 (1962), 195–272. MR 0012301 |
| Reference:
|
[5] Markov A.A.: On the existence of periodic connected topological groups.Izv. Akad. Nauk SSSR Ser. Mat. 8 (1944), 225–232 (in Russian); English transl. in: Amer. Math. Soc. Transl. (1) 8 (1962), 186–194. MR 0012300 |
| Reference:
|
[6] Nienhuys J.W.: Constructions of group topologies on abelian groups.Fund. Math. 75 (1972), 101–116. MR 0302810 |
| . |
