Units in F (Cₙ Q₁₂) and F (Cₙ D₁₂)

Let Cₙ, Qₙ and Dₙ be the cyclic group, the quaternion group and the dihedral group of order n, respectively. Recently, the structures of the unit groups of the finite group algebras of 2-groups that contain a normal cyclic subgroup of index 2 have been studied. The dihedral groups D₂₍, n 3 and the generalized quaternion groups Q₄₍, n 2 also contain a normal cyclic subgroup of index 2. The structures of the unit groups of the finite group algebras FQ₁₂, FD₁₂, F (C₂ Q₁₂) and F (C₂ D₁₂) over a finite field F are well known. In this article, we continue this investigation and establish the structures of the unit groups of the group algebras F (Cₙ Q₁₂) and F (Cₙ D₁₂) over a finite field F of characteristic p containing pᵏ elements.