A Characterization of the Unit Group in Z[T X C2]

Abstract

Describing the group of units U(ZG) of the integral group ring SG, for a finite group G, is a classical and open problem. In this note, we show that U-1(Z[T x C-2]) similar or equal to [F-97 x F-5] x [T x C-2], where T = < a, b : a(6) = 1, a(3) = b(2), ba = a(5)b > and F-97, F-97 are free groups of ranks 97 and 5, respectively.