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Paper IPM / M / 8562  


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
(1979), no. 1, 237247].
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