The probability of zero multiplication in finite group algebras

Let \mathbb{F}_qG be a finite group algebra. We denote by P(\mathbb{F}_qG) the probability that the product of two elements of \mathbb{F}_qG 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(\mathbb{F}_qG) are established where G is the cyclic group C_n, the Quaternion group Q_۸, the symmetric group S_۳ and F_q is a finite field.

کلیدواژه ها:

Unit ، zero divisor ، Wedderburn decomposition