%0 Journal Article
%T A generalization of the n^th- commutativity degree in finite groups
%J Computational Sciences and Engineering
%I University of Guilan
%Z 2783-2503
%A Pirzadeh, Mina
%A Hashemi, Mansour
%D 2022
%\ 04/17/2022
%V 2
%N 1
%P 33-40
%! A generalization of the n^th- commutativity degree in finite groups
%K Finite groups
%K Nilpotent groups
%K commutativity degree
%K GAP
%R 10.22124/cse.2022.21977.1028
%X In this paper, we study the number of solutions of commutator equation [x^{n},y]=gin 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 $G$ .
%U https://cse.guilan.ac.ir/article_5475_fc2e2e0df0565407e666aec16f5823da.pdf