The probability of zero multiplication in finite group algebras

Document Type : Research Paper


Department of Mathematics, Faculty of Science, Soran University , Kawa St, Soran, Erbil, Iraq


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 $Q_8$, the symmetric group $S_3$ and $F_q$ is a finite field.


Main Subjects

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  • Receive Date: 09 May 2023
  • Revise Date: 06 September 2023
  • Accept Date: 07 September 2023
  • Published Online: 01 June 2024