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Unit groups of group algebras of certain dihedral groups. (English) Zbl 1484.16044

Summary: In this article, we give the complete characterization of \(U(FD_4)\), \(U(FD_8)\), \(U(FD_{10})\), \(U(FD_{16})\) and \(U(FD_{20})\), where \(F\) is a finite field of characteristic \(p>0\) and \(D_n\) is the dihedral group of order \(2n\). We also find the structure of \(U(FD_{2^k})\) and \(U(FD_{5.2^k})\), when \(F\) is a finite field of characteristic 2.

MSC:

16U60 Units, groups of units (associative rings and algebras)
20C05 Group rings of finite groups and their modules (group-theoretic aspects)
16S34 Group rings
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