| Title:
|
On Butler $B(2)$-groups decomposing over two base elements (English) |
| Author:
|
De Vivo, Clorinda |
| Author:
|
Metelli, Claudia |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
50 |
| Issue:
|
2 |
| Year:
|
2009 |
| Pages:
|
165-179 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A $B(2)$-group is a sum of a finite number of torsionfree Abelian groups of rank $1$, subject to two independent linear relations. We complete here the study of direct decompositions over two base elements, determining the cases where the relations play an essential role. (English) |
| Keyword:
|
Abelian group |
| Keyword:
|
torsionfree |
| Keyword:
|
finite rank |
| Keyword:
|
Butler group |
| Keyword:
|
$B(1)$-group |
| Keyword:
|
$B(2)$-group |
| Keyword:
|
type |
| Keyword:
|
tent |
| Keyword:
|
base change |
| Keyword:
|
direct decomposition |
| Keyword:
|
typeset |
| MSC:
|
06B99 |
| MSC:
|
06F99 |
| MSC:
|
20K15 |
| idZBL:
|
Zbl 1204.20071 |
| idMR:
|
MR2537829 |
| . |
| Date available:
|
2009-08-18T12:24:20Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133426 |
| . |
| Reference:
|
[F II] Fuchs L.: Infinite Abelian Groups.Vol.II, Academic Press, London-New York, 1973. Zbl 0338.20063, MR 0349869 |
| Reference:
|
[A] Arnold D.M.: Abelian Groups and Representations of Finite Partially Ordered Sets.CMS books in Mathematics, 2, Springer, New York, 2000. Zbl 0959.16011, MR 1764257 |
| Reference:
|
[AV] Arnold D.M., Vinsonhaler C.: Finite rank Butler groups: A survey of recent results.Abelian Groups (Curacao, 1991), Lecture Notes in Pure and Applied Math., 146, Marcel Dekker, 1993, pp. 17--41. Zbl 0804.20043, MR 1217256 |
| Reference:
|
[VWW] Vinsonhaler C., Wallutis S.L., Wickless W.J.: A class of $B(2)$-groups.Comm. Algebra 33 (2005), no. 6, 2025--2037. Zbl 1077.20062, MR 2150857, 10.1081/AGB-200063348 |
| Reference:
|
[DVM 4] De Vivo C., Metelli C.: Decomposing $B(1)$-groups: an algorithm.Comm. Algebra 30 (2002), no. 12, 5621--5637. Zbl 1019.20021, MR 1941915, 10.1081/AGB-120015998 |
| Reference:
|
[DVM 8] De Vivo C., Metelli C.: On degenerate $B(2)$-groups.Houston J. Math. 32 (2006), no. 3, 633--649. MR 2247900 |
| Reference:
|
[DVM 10] De Vivo C., Metelli C.: Butler groups splitting over a base element.Colloq. Math. 109 (2007), no. 2, 297--305. Zbl 1123.20044, MR 2318525, 10.4064/cm109-2-11 |
| Reference:
|
[DVM 11] De Vivo C., Metelli C.: Settings for a study of finite rank Butler groups.J. Algebra 318 (2007), no. 1, 456--483. Zbl 1141.20032, MR 2363144, 10.1016/j.jalgebra.2007.07.024 |
| Reference:
|
[DVM 12] De Vivo C., Metelli C.: On direct decompositions of Butler $B(2)$-groups.Contributions to Module Theory, W. de Gruyter, 2007, pp. 1--18. Zbl 1191.20059 |
| Reference:
|
[DVM 14] De Vivo C., Metelli C.: The typeset of a $B(2)$-group.to appear. |
| . |
