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Rostami, Hojjat
IndoMS
Mathematics

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The Probability That an Ordered Pair of Elements is an Engel Pair Amiri, S.M. Jafarian; Rostami, Hojjat
Journal of the Indonesian Mathematical Society Volume 25 Number 2 (July 2019)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.25.2.693.121-127

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 allx 2 G. Among other results, we prove that if G is an non-abelian E-group withep(G) 16 , then G is not simple and minimal non-solvable.
Co-Authors Amiri, S.M. Jafarian