| Title:
|
A direct factor theorem for commutative group algebras (English) |
| Author:
|
Ullery, William |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
33 |
| Issue:
|
3 |
| Year:
|
1992 |
| Pages:
|
383-387 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Suppose $F$ is a field of characteristic $p\neq 0$ and $H$ is a $p$-primary abelian $A$-group. It is shown that $H$ is a direct factor of the group of units of the group algebra $F H$. (English) |
| Keyword:
|
units of group algebras |
| Keyword:
|
$A$-groups |
| MSC:
|
16S34 |
| MSC:
|
16U60 |
| MSC:
|
20C07 |
| MSC:
|
20K10 |
| idZBL:
|
Zbl 0794.16022 |
| idMR:
|
MR1209281 |
| . |
| Date available:
|
2009-01-08T17:56:40Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118507 |
| . |
| Reference:
|
[F] Fuchs L.: Infinite Abelian Groups.Volumes I and II, Academic Press, New York, 1970 and 1973. Zbl 0338.20063 |
| Reference:
|
[H1] Hill P.: The classification of $N$-groups.Houston J. Math. 10 (1984), 43-55. Zbl 0545.20042, MR 0736574 |
| Reference:
|
[H2] Hill P.: On the structure of abelian $p$-groups.Trans. Amer. Math. Soc. 288 (1985), 505-525. Zbl 0573.20053, MR 0776390 |
| Reference:
|
[HU] 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:
|
[M1] May W.: Modular group algebras of totally projective $p$-primary groups.Proc. Amer. Math. Soc. 76 (1979), 31-34. Zbl 0388.20041, MR 0534384 |
| Reference:
|
[M2] May W.: Modular group algebras of simply presented abelian groups.Proc. Amer. Math. Soc. 104 (1988), 403-409. Zbl 0691.20008, MR 0962805 |
| Reference:
|
[M] Mollov T.Zh.: Ulm invariants of Sylow $p$-subgroups of group algebras of abelian groups over fields of characteristic $p$.Pliska 2 (1981), 77-82. MR 0633857 |
| Reference:
|
[U] Ullery W.: An isomorphism theorem for commutative modular group algebras.Proc. Amer. Math. Soc. 110 (1990), 287-292. Zbl 0712.20036, MR 1031452 |
| Reference:
|
[W] Warfield R.: A classification theorem for abelian $p$-groups.Trans. Amer. Math. Soc. 210 (1975), 149-168. Zbl 0324.20058, MR 0372071 |
| . |
