Units in finite dihedral and quaternion group algebras

Abstract

Abstract Let F q G be the group algebra of a finite group G over F q = GF ( q ) . Using the Wedderburn decomposition of F 2 k D 2 n / J ( F 2 k D 2 n ) , we establish the structure of the unit group of F 2 k G when G is either D 4 n , the dihedral group of order 4 n or Q 4 n , the generalized quaternion group of order 4 n , n odd.