TY - JOUR
ID - 5475
TI - A generalization of the n^th- commutativity degree in finite groups
JO - Computational Sciences and Engineering
JA - CSE
LA - en
SN -
AU - Pirzadeh, Mina
AU - Hashemi, Mansour
AD - Department of pure Mathematics, Faculty of Mathematical Sciences, University of
Guilan, Rasht, Iran
Y1 - 2022
PY - 2022
VL - 2
IS - 1
SP - 33
EP - 40
KW - Finite groups
KW - Nilpotent groups
KW - commutativity degree
KW - GAP
DO - 10.22124/cse.2022.21977.1028
N2 - 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 $G$ .
UR - https://cse.guilan.ac.ir/article_5475.html
L1 - https://cse.guilan.ac.ir/article_5475_fc2e2e0df0565407e666aec16f5823da.pdf
ER -