Abstract
Denote by Q m the generalized quaternion group of order 4m. Let R(Q m ) be its complex representation ring, and Δ(Q m ) its augmentation ideal. In this paper, the author gives an explicit Z-basis for the Δn(Q m ) and determines the isomorphism class of the n-th augmentation quotient \(\frac{{{\Delta ^n}\left( {{Q_m}} \right)}}{{{\Delta ^{n + 1}}\left( {{Q_m}} \right)}}\) for each positive integer n.
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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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Chang, S. Augmentation quotients for complex representation rings of generalized quaternion groups. Chin. Ann. Math. Ser. B 37, 571–584 (2016). https://doi.org/10.1007/s11401-016-1017-x
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DOI: https://doi.org/10.1007/s11401-016-1017-x