| Title:
|
Subgroups of odd depth—a necessary condition (English) |
| Author:
|
Burciu, Sebastian |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
63 |
| Issue:
|
4 |
| Year:
|
2013 |
| Pages:
|
1039-1048 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper gives necessary and sufficient conditions for subgroups with trivial core to be of odd depth. We show that a subgroup with trivial core is an odd depth subgroup if and only if certain induced modules from it are faithful. Algebraically this gives a combinatorial condition that has to be satisfied by the subgroups with trivial core in order to be subgroups of a given odd depth. The condition can be expressed as a certain matrix with $\{0,1\}$-entries to have maximal rank. The entries of the matrix correspond to the sizes of the intersections of the subgroup with any of its conjugate. (English) |
| Keyword:
|
depth of group algebras |
| Keyword:
|
finite group |
| Keyword:
|
faithful representation |
| MSC:
|
34B16 |
| MSC:
|
34C25 |
| idZBL:
|
Zbl 1299.20001 |
| idMR:
|
MR3165513 |
| DOI:
|
10.1007/s10587-013-0070-9 |
| . |
| Date available:
|
2014-01-28T14:15:23Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143615 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| . |
