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http://dx.doi.org/10.4134/BKMS.b150526

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

Bilgin, Tevfik (Department of Mathematics Fatih University)
Kusmus, Omer (Department of Mathematics Yuzuncu Yil University)
Low, Richard M. (Department of Mathematics San Jose State University)
Publication Information
Bulletin of the Korean Mathematical Society / v.53, no.4, 2016 , pp. 1105-1112 More about this Journal
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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