English

Characterizing finite solvable groups through the nilpotency probability

Group Theory 2026-04-07 v1

Abstract

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

Keywords

Cite

@article{arxiv.2604.04534,
  title  = {Characterizing finite solvable groups through the nilpotency probability},
  author = {Andrea Lucchini},
  journal= {arXiv preprint arXiv:2604.04534},
  year   = {2026}
}