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arXiv · 2604.04534

Characterizing finite solvable groups through the nilpotency probability

Andrea Lucchini
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Abstract

Given a finite group $G$, we denote by $\nu(G)$ the probability that two randomly chosen elements of $G$ generate a nilpotent subgroup. We prove that if $\nu(G)>1/12,$ then $G$ is solvable.

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Andrea Lucchini. 2026-04-06. Characterizing finite solvable groups through the nilpotency probability. https://arxiv.org/abs/2604.04534

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