University of Guilan Computational Sciences and Engineering 2783-2503 2 1 2022 04 17 A generalization of the n^th- commutativity degree in finite groups 33 40 5475 10.22124/cse.2022.21977.1028 EN Mina Pirzadeh Department of pure Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran Mansour Hashemi Department of pure Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran Journal Article 2022 03 10 In this paper, we study the number of solutions of commutator equation [x^{n},y]=g<br /><br />in two classes of finite groups. For $g in G$ we consider $ rho^{n}_g(G)={(x,y)| x,yin G, [x^{n},y]=g}$ . Then the probability that the commutator equation [x^{n},y]=g has a solution in a finite group $G$, written , $P^{n}_g(G)$ is equal to $frac{|rho^{n}_{g}(G)|}{|G|^2}$ . By using the numerical solutions of the equation $xy - zu equiv t(bmod~n)$ we derive formulas for calculating the probability of $P^{n}_g(G)$, for some finite groups $G$ . https://cse.guilan.ac.ir/article_5475_fc2e2e0df0565407e666aec16f5823da.pdf