Group algebras of polynomial growth (Q581512)

Let A be a connected, basic, finite-dimensional algebra over an algebraically closed field of characteristic p, and let G be a finite group. The author describes when the group algebra AG is of infinite representation type but tame, domestic, or of polynomial growth. When p is not a divisor of \(| G|\), AG has one of these properties just when A does. Otherwise, the conditions are severely restrictive, especially if \(A\neq k\). The details are too complicated to reproduce here. [Reviewer's remark: In part (ii) of Theorem 3, \(p=2\) should be assumed.]