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Probability that the commutator of two group elements is equal to a given element |
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| Authors: | MR Pournaki R Sobhani |
| Institution: | a Department of Mathematical Sciences, Sharif University of Technology, P.O. Box 11155-9415, Tehran, Iran b School of Mathematics, Institute for Studies in Theoretical Physics and Mathematics, P.O. Box 19395-5746, Tehran, Iran c Department of Mathematical Sciences, Isfahan University of Technology, P.O. Box 85145, Isfahan, Iran |
| Abstract: | In this paper we study the probability that the commutator of two randomly chosen elements in a finite group is equal to a given element of that group. Explicit computations are obtained for groups G which |G′| is prime and G′≤Z(G) as well as for groups G which |G′| is prime and G′∩Z(G)=1. This paper extends results of Rusin see D.J. Rusin, What is the probability that two elements of a finite group commute? Pacific J. Math. 82 (1) (1979) 237-247]. |
| Keywords: | Primary 20D99 20F12 20F35 secondary 20C15 20D60 |
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