The structure of U(F (Cn × D8))

Abstract

Let \(D_n\) be the dihedral group of order \(n\). The structures of the unit groups of the finite group algebras \(FD_8\) and \(F(C_2 \times D_8)\) over a field \(F\) of characteristic 2 are given in: L. Creedon, J. Gildea. The structure of the unit group of the group algebra \(F_{2^k}D_{8}\). Canad. Math. Bull. 54, 2 (2011), 237–243 and J. Gildea. Units of the group algebra \(F_{2^k}(C_{2} \times D_{8})\). J. Algebra Appl. 10, 4 (2011), 643–647, respectively. In this article, we establish the structure of the unit group of the group algebra \(F(C_n \times D_8)\), \(n \geq 1\) over a finite field \(F\) of characteristic \(p\) containing \(q=p^k\) elements.