The probability of zero multiplication in finite group algebras

Mohammed Salih, Haval M.

doi:10.22108/ijgt.2023.137640.1842

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	The probability of zero multiplication in finite group algebras
International Journal of Group Theory
مقاله 6، دوره 13، شماره 2، شهریور 2024، صفحه 189-194 اصل مقاله (456.54 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2023.137640.1842
نویسنده
Haval M. Mohammed Salih^*
Department of Mathematics, Faculty of Science, Soran University , Kawa St, Soran, Erbil, Iraq
چکیده
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.
کلیدواژه‌ها
Unit؛ Zero divisor؛ Wedderburn decomposition

مراجع
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The probability of zero multiplication in finite group algebras