The probability of zero multiplication in finite group algebras

Let FqG be a finite group algebra. We denote by P(FqG) the probability that the product of two elements of FqG be zero. In this paper, we obtain several results on this probability including a computing formula and characterizations. In particular, the computing formula for the P(FqG) are established where G is the cyclic group Cn, the Quaternion group Q8, the symmetric group S3 and Fq is a finite field.