Abstract Given a finite group G, we denote by ν (G) (G) nu left parenthesis upper G right parenthesis the probability that two randomly chosen elements of G generate a nilpotent subgroup. We prove that if ν (G) > 1 / 12, (G) > 1/12, nu left parenthesis upper G right parenthesis greater than 1 divided by 12 comma then G is solvable.
Andrea Lucchini (Mon,) studied this question.
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