On the commutativity degree of a group algebra

The aim of this paper is to give a generalization of the concept of commutativity degree of a finite group G (denoted by d ( G )), to the concept of commutativity degree of a group algebra F [ G ], where G is a finite group and F is a finite field. We prove that two isoclinic groups for which the order of their centers are equal have the same commutativity degree. Finally, we give some lower and upper bounds for the commutativity degree of group algebra F [ G ] in terms of the order of G , the order of F and d ( G ).