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A characterization of the unit group in $\mathbb{Z}[T \times C_2]$

Tevfik Bilgin|Omer Kusmus|Richard M. Low
대한수학회 (The Korean Mathematical Society)|2016.07|대한수학회보 (Bulletin of the KMS)|제53권 제4호|pp. 1105-1112

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참고문헌

키워드

integral group ringunit problem
주제분류수학

초록

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 $U_1(\mathbb{Z}[T \times C_2]) \cong [F_{97} \rtimes F_5] \rtimes [T \times C_2]$, 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.

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 $U_1(\mathbb{Z}[T \times C_2]) \cong [F_{97} \rtimes F_5] \rtimes [T \times C_2]$, 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.

참고문헌 (24)

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