| Title:
|
Principal blocks and $p$-radical groups (English) |
| Author:
|
Hu, Xiaohan |
| Author:
|
Zeng, Jiwen |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
66 |
| Issue:
|
2 |
| Year:
|
2016 |
| Pages:
|
431-444 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $G$ be a finite group and $k$ a field of characteristic $p > 0$. In this paper, we obtain several equivalent conditions to determine whether the principal block $B_{0}$ of a finite $p$-solvable group $G$ is $p$-radical, which means that $B_{0}$ has the property that $e_{0} (k_P)^G $ is semisimple as a $kG$-module, where $P$ is a Sylow $p$-subgroup of $G$, $k_{P}$ is the trivial $kP$-module, $(k_{P})^{G}$ is the induced module, and $e_{0}$ is the block idempotent of $B_{0}$. We also give the complete classification of a finite $p$-solvable group $G$ which has not more than three simple $B_{0}$-modules where $B_0$ is $p$-radical. (English) |
| Keyword:
|
principal block |
| Keyword:
|
$p$-radical group |
| Keyword:
|
$p$-radical block |
| MSC:
|
20C05 |
| MSC:
|
20C20 |
| idZBL:
|
Zbl 06604477 |
| idMR:
|
MR3519612 |
| DOI:
|
10.1007/s10587-016-0266-x |
| . |
| Date available:
|
2016-06-16T12:52:10Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145734 |
| . |
| Reference:
|
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