# A CHARACTERIZATION OF THE UNIT GROUP IN ℤ[T×C2]

• Bilgin, Tevfik ;
• Kusmus, Omer ;
• Low, Richard M.
• Published : 2016.07.31
• 37 6

#### Abstract

Describing the group of units $U({\mathbb{Z}}G)$ of the integral group ring ${\mathbb{Z}}G$, for a finite group G, is a classical and open problem. In this note, we show that $$U_1({\mathbb{Z}}[T{\times}C_2]){\sim_=}[F_{97}{\rtimes}F_5]{\rtimes}[T{\times}C_2]$$, where $T={\langle}a,b:a^6=1,a^3=b^2,ba=a^5b{\rangle}$ and $F_{97}$, $F_5$ are free groups of ranks 97 and 5, respectively.

#### Keywords

integral group ring;unit problem

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