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

Abstract

Let F be a finite field of characteristic p. There are three nonisomorphic non-abelian groups of order 30. The structure of U (F (C 5 ×D 6 )) for p = 3 is given in [

The structure of the unit group of the group algebra F(C₃ × D₁₀)

“…given in [10]. In this article, we provide an explicit description for the Wedderburn decomposition of / ( ), = 3 × 10 and a finite field of characteristic ̸ = 3, using the theory developed by Ferraz [3] and with the help of this description we obtain the structure of ( ( 3 × 10 )).…”

“…

Letbe the dihedral group of order . The structure of the unit group ( ( 3 × 10)) of the group algebra ( 3 × 10) over a finite field of characteristic 3 is given in [10]. In this article, the structure of ( ( 3 × 10)) is obtained over any finite field of characteristic ̸ = 3.

…”

“…Many authors [1,4,5,7,[9][10][11][12] have studied the structure of ( ) for a finite group and for a finite field . The structure of ( ( 3 × 10 )) for = 3 is…”