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
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
[1] M. A. Esmkhani and S. M. Jafarian Amiri, The probability that the multiplication of two ring elements is zero, J. Algebra Appl., 17 (2018) 9 pp. [2] N. Makhijani, R. K. Sharma and J. B. Srivastava, The unit group of algebra of circulant matrices, Int. J. Group Theory, 3 no. 4 (2014) 13–16. [3] J. Gildea, On the order of U (Fpk D2pm ), Int. J. Pure Appl. Math., 46 (2008) 267–272. [4] G. Tang and Y. Gao, The unit groups of F G of groups with order 12, Int. J. Pure Appl. Math., 73 (2011) 143–158. [5] H. M. Mohammed Salih, On the probability of zero divisor elements in group rings Int. J. Group Theory, 11 no. 4 (2022) 253–257. [6] C. P. Milies and S. K. Sehgal, An introduction to group rings, Springer Science and Business Media, 1, Kluwer Academic publishers Dordrecht/Boston/London, 2002. [7] H. Cheraghpour and N. G. Ghosseiri, On the idempotents, nilpotents, units and zero-divisors of finite rings. Linear Multilinear Algebra, 67 (2019) 327–336. [8] F. E. Brochero Martinez, Structure of finite dihedral group algebra, Finite Fields Appl., 35 (2015) 204-214. [9] R. Lidl and H. Niederreiter, Finite fields, Cambridge University Press, 1997. [10] S. Perlis and G. L. Walker, Abelian group algebras of finite order, Trans. Amer. Math. Soc., 68 (1950) 420–426. [11] D. David, The probability of zero multiplication in finite rings, Bull. Aust. Math. Soc., 106 (2022) 83–88.
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The probability of zero multiplication in finite group algebras