Main Article Content
Abstract
Let G be a nite group. We denote by ep(G) the probability that
[x;n y] = 1 for two randomly chosen elements x and y of G and some posi-
tive integer n. For x 2 G we denote by EG(x) the subset fy 2 G : [y;n x] =
1 for some integer ng. G is called an E-group if EG(x) is a subgroup of G for all
x 2 G. Among other results, we prove that if G is an non-abelian E-group with
ep(G) > 1
6 , then G is not simple and minimal non-solvable.
[x;n y] = 1 for two randomly chosen elements x and y of G and some posi-
tive integer n. For x 2 G we denote by EG(x) the subset fy 2 G : [y;n x] =
1 for some integer ng. G is called an E-group if EG(x) is a subgroup of G for all
x 2 G. Among other results, we prove that if G is an non-abelian E-group with
ep(G) > 1
6 , then G is not simple and minimal non-solvable.
Keywords
nite group
E-group
Engel element.
Article Details
How to Cite
Amiri, S. J., & Rostami, H. (2019). The Probability That an Ordered Pair of Elements is an Engel Pair. Journal of the Indonesian Mathematical Society, 25(2), 121–127. https://doi.org/10.22342/jims.25.2.693.121-127
