@article {
author = {Pirzadeh, Mina and Hashemi, Mansour},
title = {A generalization of the n^th- commutativity degree in finite groups},
journal = {Computational Sciences and Engineering},
volume = {2},
number = {1},
pages = {33-40},
year = {2022},
publisher = {University of Guilan},
issn = {2783-2503},
eissn = {2783-2503},
doi = {10.22124/cse.2022.21977.1028},
abstract = {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 $G$ .},
keywords = {Finite groups,Nilpotent groups,commutativity degree,GAP},
url = {https://cse.guilan.ac.ir/article_5475.html},
eprint = {https://cse.guilan.ac.ir/article_5475_fc2e2e0df0565407e666aec16f5823da.pdf}
}