Document Type : Original Article

Authors

Department of pure Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran

Abstract

In this paper, we study the number of solutions of commutator equation [x^{n},y]=g

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\$ .

Keywords

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