THE GROUP OF UNITS OF GROUP ALGEBRAS OF GROUPS $D_{30}$ AND $C_3 \times D_{10}$ OVER A FINITE FIELD OF CHARACTERISTIC $3$

Authors : Meena SAHAI, Sheere Farhat ANSARI

Pages : 165-174

Doi:10.24330/ieja.852146

View : 11 | Download : 11

Publication Date : 2021-01-05

Article Type : Research Paper

Abstract :Let $F$ be a finite field of characteristic $p$. There are three non-isomorphic non-abelian groups of order $30$. The structure of $Uinsert ignore into journalissuearticles values(Finsert ignore into journalissuearticles values(C_5 \times D_6););$ for $p=3$ is given in [J. Gildea and R. Taylor, Int. Electron. J. Algebra, 24 insert ignore into journalissuearticles values(2018);, 62-67]. In this article, we give the structure of $Uinsert ignore into journalissuearticles values(FD_{30});$ and $Uinsert ignore into journalissuearticles values(Finsert ignore into journalissuearticles values(C_3 \times D_{10}););$ for $p=3$.
Keywords : Group ring, unit group, dihedral group