On the units of integral group ring of Cn×C₆

Abstract

There are many kind of open problems with varying difficulty on units in a given integral group ring. In this note, we characterize the unit group of the integral group ring of Cn×C₆ where Cn=⟨a:aⁿ=1⟩ and C₆=⟨x:x⁶=1⟩. We show that U₁(Z[Cn×C₆]) can be expressed in terms of its 4 subgroups. Furthermore, forms of units in these subgroups are described by the unit group U₁(ZCn).