Some restrictions on the probability of generating nilpotent subgroups

Several authors have studied the probability that randomly chosen elements of a finite group generate a nilpotent subgroup. In the present article, we consider the probability that $n + 1$ randomly chosen elements of a finite group generate a nilpotent subgroup of class at most $c$, where $n$ and $c$ are positive integers. We show also a result of invariance for two finite $c$-isoclinic groups in the sense of Hekster. Our proofs areccharacter–free and follow some classical methods in literature.