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

Year 2021, Volume: 29 Issue: 29, 165 - 174, 05.01.2021

Meena Sahaı Sheere Farhat Ansarı

https://doi.org/10.24330/ieja.852146

Abstract

Let $F$ be a finite field of characteristic $p$.
There are three non-isomorphic non-abelian groups of order $30$.
The structure of $U(F(C_5 \times D_6))$ for $p=3$ is given in [J.
Gildea and R. Taylor, Int. Electron. J. Algebra, 24 (2018),
62-67]. In this article, we give the structure of $U(FD_{30})$ and
$U(F(C_3 \times D_{10}))$ for $p=3$.

Keywords

Group ring, unit group, dihedral group

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