The Probability That an Ordered Pair of Elements is an Engel Pair

Hojjat Rostami


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.


nite group, E-group, Engel element.

Full Text:




  • There are currently no refbacks.

Journal of the Indonesian Mathematical Society
Mathematics Department, Universitas Gadjah Mada
Senolowo, Sinduadi, Mlati, Sleman Regency, Special Region of Yogyakarta 55281, Telp. (0274) 552243

p-ISSN: 2086-8952 | e-ISSN: 2460-0245

Journal of the Indonesian Mathematical Society is licensed under a Creative Commons Attribution 4.0 International License

web statistics
View My Stats