An Upper Bound for the Probability of Generating a Finite Nilpotent Group

• Published in: Kyungpook mathematical journal Vol. 63; no. 2; pp. 167 - 173
• Main Authors: Halimeh Madadi, Seyyed Majid Jafarian Amiri, Hojjat Rostami
• Format: Journal Article
• Language: Korean
• Published: 2023
• Subjects: Nilpotent subgroup; Soluble group; Probability

Let G be a finite group and let ν(G) be the probability that two randomly selected elements of G produce a nilpotent group. In this article we show that for every positive integer n > 0, there is a finite group G such that ${\nu}(G)={\frac{1}{n}}$. We also classify all groups G with ${\nu}(G)={\f...