Characterising Finite Solvable Groups Through the Nilpotency Probability

Given a finite group G , we denote by ν ( G ) ν (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 , ν (G)> 1/12, nu left parenthesis upper G right parenthesis greater than 1 divided by 12 comma then G is solvable.