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| Augmentation Quotients for Complex Representation Rings of GeneralizedQuaternion Groups |
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Citation： |
Shan CHANG.Augmentation Quotients for Complex Representation Rings of GeneralizedQuaternion Groups[J].Chinese Annals of Mathematics B,2016,37(4):571~584 |
| Page view： 1940
Net amount： 1320 |
Authors： |
Shan CHANG; |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (Nos.11226066, 11401155) and Anhui Provincial
Natural Science Foundation (No.1308085QA01). |
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| Abstract： |
Denote by $\mathcal{Q}_m$ the generalized quaternion group of order
$4m$. Let $\mathcal{R}(\mathcal{Q}_m)$ be its complex representation
ring, and $\Delta(\mathcal{Q}_m)$ its augmentation ideal. In this
paper, the author gives an explicit $\mathbb{Z}$-basis for the
$\Delta^n(\mathcal{Q}_m)$ and determines the isomorphism class of
the $n$-th augmentation quotient
$\frac{\Delta^n(\mathcal{Q}_m)}{\Delta^{n+1}(\mathcal{Q}_m)}$ for
each positive integer $n$. |
Keywords： |
Generalized quaternion groups, Representation ring, Augmentation
quotients |
Classification： |
16S34, 20C05 |
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