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.