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

S.M. Jafarian Amiri (1), Hojjat Rostami (2)
(1) Department of Mathematics, University of Zanjan, Iran, Islamic Republic of,
(2) Department of Mathematics, Faculty of Sciences, University of Zan- jan,P.O.Box 45371-38791, Zanjan, Iran, Iran, Islamic Republic of

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.

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Authors

S.M. Jafarian Amiri
Hojjat Rostami
h.rostami5991@gmail.com (Primary Contact)
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
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