| Title:
|
Almost coproducts of finite cyclic groups (English) |
| Author:
|
Hill, Paul |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
36 |
| Issue:
|
4 |
| Year:
|
1995 |
| Pages:
|
795-804 |
| . |
| Category:
|
math |
| . |
| Summary:
|
A new class of $p$-primary abelian groups that are Hausdorff in the $p$-adic topology and that generalize direct sums of cyclic groups are studied. We call this new class of groups almost coproducts of cyclic groups. These groups are defined in terms of a modified axiom 3 system, and it is observed that such groups appear naturally. For example, $V(G)/G$ is almost a coproduct of finite cyclic groups whenever $G$ is a Hausdorff $p$-primary group and $V(G)$ is the group of normalized units of the modular group algebra over $Z/pZ$. Several results are obtained concerning almost coproducts of cyclic groups including conditions on an ascending chain that implies that the union of the chain is almost a coproduct of cyclic groups. (English) |
| Keyword:
|
primary groups |
| Keyword:
|
coproduct of cyclic groups |
| Keyword:
|
almost coproducts |
| Keyword:
|
third axiom of countability |
| MSC:
|
20K10 |
| MSC:
|
20K25 |
| MSC:
|
20K45 |
| idZBL:
|
Zbl 0845.20038 |
| idMR:
|
MR1378700 |
| . |
| Date available:
|
2009-01-08T18:21:46Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118806 |
| . |
| Reference:
|
[F] Fuchs L.: Infinite Abelian Groups.vol. 2, Academic Press, New York, 1973. Zbl 0338.20063, MR 0349869 |
| Reference:
|
[H1] Hill P.: On the classification of abelian groups.photocopied manuscript, 1967. |
| Reference:
|
[H2] Hill P.: Primary groups whose subgroups of smaller cardinality are direct sums of cyclic groups.Pacific Jour. Math. 42 (1972), 63-67. Zbl 0251.20057, MR 0315018 |
| Reference:
|
[H3] Hill P.: Units of commutative modular group algebras.Jour. Pure and Applied Algebra, to appear. Zbl 0806.16033, MR 1282838 |
| Reference:
|
[HM] Hill P., Megibben C.: On the theory and classification of abelian $p$-groups.Math. Zeit. 190 (1985), 17-38. Zbl 0535.20031, MR 0793345 |
| Reference:
|
[HU1] Hill P., Ullery W.: A note on a theorem of May concerning commutative group algebras.Proc. Amer. Math. Soc. 110 (1990), 59-63. Zbl 0704.20007, MR 1039530 |
| Reference:
|
[HU2] Hill P., Ullery W.: Almost totally projective groups.preprint. Zbl 0870.20035, MR 1388614 |
| Reference:
|
[K] Kulikov L.: On the theory of abelian groups of arbitrary power (Russian).Mat. Sb. 16 (1945), 129-162. MR 0018180 |
| . |
