Characterization of U1(Z[CnXK4])

Ismail Gokhan Kelebek, Tevfik Bilgin

Abstract

Constructing the group of units U(ZG) of the integral group ring ZG, for a nitegroup G, is a classical but open problem. In this study, it is shown that U1(Z[Cn x K4]) =U1(ZCn) (1 + K^x) x (1 + K^y) x (1 + K^xy). This structure theorem is applied to give precise characterization of U1(Z[Cn x K4]) for cyclic groups C5 and C7.

Keywords

Integral group ring, unit problem, generators of unit group

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