| Title:
|
A note on a theorem of Megibben (English) |
| Author:
|
Danchev, Peter |
| Author:
|
Keef, Patrick |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
44 |
| Issue:
|
3 |
| Year:
|
2008 |
| Pages:
|
245-249 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that pure subgroups of thick Abelian $p$-groups which are modulo countable are again thick. This generalizes a result due to Megibben (Michigan Math. J. 1966). Some related results are also established. (English) |
| Keyword:
|
thick groups |
| Keyword:
|
pure subgroups |
| Keyword:
|
countable extensions |
| Keyword:
|
divisible groups |
| Keyword:
|
bounded groups |
| MSC:
|
20K10 |
| MSC:
|
20K27 |
| idZBL:
|
Zbl 1204.20070 |
| idMR:
|
MR2462980 |
| . |
| Date available:
|
2009-01-29T09:15:11Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119764 |
| . |
| Reference:
|
[1] Benabdallah, K., Wilson, R.: Thick groups and essentially finitely indecomposable groups.Canad. J. Math. 30 (3) (1978), 650–654. Zbl 0399.20049, MR 0492006, 10.4153/CJM-1978-056-9 |
| Reference:
|
[2] Danchev, P. V.: Commutative group algebras of thick abelian $p$-groups.Indian J. Pure Appl. Math. 36 (6) (2005), 319–328. Zbl 1088.20001, MR 2178344 |
| Reference:
|
[3] Danchev, P. V.: Generalized Dieudonné and Hill criteria.Portugal. Math. 65 (1) (2008), 121–142. Zbl 1146.20034, MR 2387091, 10.4171/PM/1802 |
| Reference:
|
[4] Danchev, P. V., Keef, P. W.: Generalized Wallace theorems.Math. Scand., to appear. MR 2498370 |
| Reference:
|
[5] Keef, P. W.: Primary abelian groups admitting only small homomorphisms.Commun. Algebra 23 (10) (1995), 3615–3626. Zbl 0835.20072, MR 1348253, 10.1080/00927879508825421 |
| Reference:
|
[6] Megibben, C. K.: Large subgroups and small homomorphisms.Michigan Math. J. 13 (2) (1966), 153–160. Zbl 0166.02502, MR 0195939, 10.1307/mmj/1028999539 |
| Reference:
|
[7] Nunke, R. J.: Homology and direct sums of countable abelian groups.Math. Z. 101 (3) (1967), 182–212. Zbl 0173.02401, MR 0218452, 10.1007/BF01135839 |
| Reference:
|
[8] Pierce, R. S.: Homomorphisms of Primary Abelian Groups, Topics in Abelian Groups.(Proc. Sympos., New Mexico State Univ., 1962), Scott, Foresman and Co., Chicago, Illinois, 1963, pp. 215–310. MR 0177035 |
| Reference:
|
[9] Wallace, K. D.: 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 |
| . |
