Given a finite group G, we denote by ν(G) the probability that two randomly chosen elements of G generate a nilpotent subgroup. We prove that if ν(G) > 1/12, then G is solvable.
CHARACTERISING FINITE SOLVABLE GROUPS THROUGH THE NILPOTENCY PROBABILITY
Lucchini A.
2026
Abstract
Given a finite group G, we denote by ν(G) the probability that two randomly chosen elements of G generate a nilpotent subgroup. We prove that if ν(G) > 1/12, then G is solvable.
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