| Title:
|
Isotype subgroups of mixed groups (English) |
| Author:
|
Megibben, Charles |
| Author:
|
Ullery, William |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
42 |
| Issue:
|
3 |
| Year:
|
2001 |
| Pages:
|
421-442 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we initiate the study of various classes of isotype subgroups of global mixed groups. Our goal is to advance the theory of $\Sigma$-isotype subgroups to a level comparable to its status in the simpler contexts of torsion-free and $p$-local mixed groups. Given the history of those theories, one anticipates that definitive results are to be found only when attention is restricted to global $k$-groups, the prototype being global groups with decomposition bases. A large portion of this paper is devoted to showing that primitive elements proliferate in $\Sigma$-isotype subgroups of such groups. This allows us to establish the fundamental fact that finite rank $\Sigma$-isotype subgroups of $k$-groups are themselves $k$-groups. (English) |
| Keyword:
|
global $k$-group |
| Keyword:
|
$\Sigma$-isotype subgroup |
| Keyword:
|
$\ast$-isotype subgroup |
| Keyword:
|
knice subgroup |
| Keyword:
|
primitive element |
| Keyword:
|
$\ast$-valuated coproduct |
| MSC:
|
20K21 |
| MSC:
|
20K27 |
| idZBL:
|
Zbl 1102.20037 |
| idMR:
|
MR1859590 |
| . |
| Date available:
|
2009-01-08T19:11:21Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119257 |
| . |
| Reference:
|
Hill P., Megibben C.: Torsion free groups.Trans. Amer. Math. Soc. 295 (1986), 735-751. Zbl 0597.20047, MR 0833706 |
| Reference:
|
Hill P., Megibben C.: Knice subgroups of mixed groups.Abelian Group Theory Gordon-Breach New York (1987), 89-109. Zbl 0653.20057, MR 1011306 |
| Reference:
|
Hill P., Megibben C.: Pure subgroups of torsion-free groups.Trans. Amer. Math. Soc. 303 (1987), 765-778. Zbl 0627.20028, MR 0902797 |
| Reference:
|
Hill P., Megibben C.: Mixed groups.Trans. Amer. Math. Soc. 334 (1992), 121-142. Zbl 0798.20050, MR 1116315 |
| Reference:
|
Hill P., Megibben C., Ullery W.: $\Sigma$-isotype subgroups of local $k$-groups.Contemp. Math. 273 (2001), 159-176. Zbl 0982.20038, MR 1817160 |
| . |
