Nonnilpotent subsets in the susuki groups

Abstract

Let G be a group and N be the class of nilpotent groups. A subset A of G is said to be nonnilpotent if for any two distinct elements a and b in A, ha, bi 62 N. If, for any other nonnilpotent subset B in G, |A| ? |B|, 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 field with q elements and PGL(2, q) is the projective general linear group of degree 2 over the finite field of size q, respectively.