Augmentation Quotients for Complex Representation Rings of GeneralizedQuaternion Groups

Denote by $mathcal{Q}_m$ the generalized quaternion group of order$4m$. Let $mathcal{R}(mathcal{Q}_m)$ be its complex representationring, and $Delta(mathcal{Q}_m)$ its augmentation ideal. In thispaper, the author gives an explicit $mathbb{Z}$-basis for the$Delta^n(mathcal{Q}_m)$ and determines the isomorphism class ofthe $n$-th augmentation quotient$frac{Delta^n(mathcal{Q}_m)}{Delta^{n+1}(mathcal{Q}_m)}$ foreach positive integer $n$.