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
مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 16 شهریور 1402 اصل مقاله (463.62 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