University of GuilanComputational Sciences and Engineering2783-25032120220417A generalization of the n^th- commutativity degree in finite groups3340547510.22124/cse.2022.21977.1028ENMinaPirzadehDepartment of pure Mathematics, Faculty of Mathematical Sciences, University of
Guilan, Rasht, IranMansourHashemiDepartment of pure Mathematics, Faculty of Mathematical Sciences, University of
Guilan, Rasht, IranJournal Article20220310In 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