Derivations of Non-Commutative Group Algebras

In this paper, we study the derivations of group algebras of some important groups, namely, Dihedral (Formula: see text), Dicyclic (Formula: see text) and Semi-dihedral (Formula: see text). First, we explicitly classify all inner derivations of a group algebra Formula: see text of a finite group Formula: see text over an arbitrary field Formula: see text. Then we classify all Formula: see text-derivations of the group algebras Formula: see text, Formula: see text and Formula: see text when Formula: see text is a field of characteristic Formula: see text or an odd rational prime Formula: see text by giving the dimension and an explicit basis of these derivation algebras. We explicitly describe all inner derivations of these group algebras over an arbitrary field. Finally, we classify all derivations of the above group algebras when Formula: see text is an algebraic extension of a prime field.