Induced representations of finite ring groups (Q1101529)

The notion of a ring group was introduced by G. I. Kac in the early 60ies in order to generalize Pontryagin's duality theory to the noncommutative case [see e.g.: \textit{G. I. Kac} and \textit{V. G. Palyutkin}, Tr. Mosk. Mat. O-va 15, 224-261 (1966; Zbl 0218.43005)]. A ring group is a sort of \({\mathbb{C}}\)-coalgebra in which matrix representation theory may be developed. In the paper under review the author extends to ring groups theorems by Frobenius and Artin on induced representations of finite groups.