IJPAM: Volume 73, No. 2 (2011)

THE UNIT GROUPS OF $FG$ OF GROUPS WITH ORDER 12

Tang Gaohua$^1$, Gao Yanyan$^2$
School of Mathematical Sciences
Guangxi Teachers Education University
Nanning, Guangxi 530023, P.R. CHINA


Abstract. Note that there are five mutually non-isomorphic groups of order 12: two decomposable Abelian groups $G_{1}$ $\cong$ $C_{3}\times C_{4}$ and $G_{2}$ $\cong$ $C_{3}$$\times$$K_{4}$; three indecomposable non-Abelian groups $A_4$, $Q_{12}$ and $D_{12}$. For a finite field $F$, the structure of $\mathscr{U}(FA_4)$ was determined by R.K. Sharma, J.B. Srivastava and M. Khan in 2007. In this paper, we determine the structure of the unit group $\mathscr{U}(FG)$ of the group ring $FG$, where $F$ is a finite field, and $G$= $G_1$, $G_2$, $Q_{12}$ or $D_{12}$.

Received: June 13, 2011

AMS Subject Classification: 16S34, 16U60, 20C05

Key Words and Phrases: finite field, group ring, unit group

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 73
Issue: 2