ON THE PROBABILITY OF GENERATING NILPOTENT SUBGROUPS IN A FINITE GROUP
ON THE PROBABILITY OF GENERATING NILPOTENT SUBGROUPS IN A FINITE GROUP
Let $G$ be a finite group. We denote by ${\it\nu}(G)$ the probability that two randomly chosen elements of $G$ generate a nilpotent subgroup and by $\text{Nil}_{G}(x)$ the set of elements $y\in G$ such that $\langle x,y\rangle$ is a nilpotent subgroup. A group $G$ is called an ${\mathcal{N}}$ -group if $\text{Nil}_{G}(x)$ …