Augmentation quotients for complex representation rings of generalized quaternion groups

Abstract

Denote by Qm the generalized quaternion group of order 4m. Let R(Qm) be its complex representation ring, and Δ(Qm) its augmentation ideal. In this paper, the author gives an explicit Z-basis for the Δn(Qm) 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.