| Title:
|
Augmentation quotients for Burnside rings of generalized dihedral groups (English) |
| Author:
|
Chang, Shan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
66 |
| Issue:
|
4 |
| Year:
|
2016 |
| Pages:
|
1165-1175 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $H$ be a finite abelian group of odd order, $\mathcal {D}$ be its generalized dihedral group, i.e., the semidirect product of $C_2$ acting on $H$ by inverting elements, where $C_2$ is the cyclic group of order two. Let $\Omega (\mathcal {D})$ be the Burnside ring of $\mathcal {D}$, $\Delta (\mathcal {D})$ be the augmentation ideal of $\Omega (\mathcal {D})$. Denote by $\Delta ^n(\mathcal {D})$ and $Q_n(\mathcal {D})$ the $n$th power of $\Delta (\mathcal {D})$ and the $n$th consecutive quotient group $\Delta ^n(\mathcal {D})/\Delta ^{n+1}(\mathcal {D})$, respectively. This paper provides an explicit $\mathbb {Z}$-basis for $\Delta ^n(\mathcal {D})$ and determines the isomorphism class of $Q_n(\mathcal {D})$ for each positive integer $n$. (English) |
| Keyword:
|
generalized dihedral group |
| Keyword:
|
Burnside ring |
| Keyword:
|
augmentation ideal |
| Keyword:
|
augmentation quotient |
| MSC:
|
16S34 |
| MSC:
|
20C05 |
| idZBL:
|
Zbl 06674868 |
| idMR:
|
MR3572929 |
| DOI:
|
10.1007/s10587-016-0316-4 |
| . |
| Date available:
|
2016-11-26T20:56:57Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145925 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| . |
