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.