Let G be a group and N be the class of all nilpotent groups. A subset A of G is said to be nonnilpotent if for any two distinct elements a and b in A, ⟨a; b⟩ ̸2 N. If, for any other nonnilpotent subset B in G, jAj jBj, then A is said to be a maximal nonnilpotent subset and the cardinality of this subset (if it exists) is denoted by !(NG). In this paper, among other results, we obtain !(NSuz(q)) and !(NPGL(2;q)), where Suz(q) is the Suzuki simple group over the eld with q elements and PGL(2; q) is the projective general linear group of degree 2 over the nite eld with q elements, respectively
