Nonnilpotent subsets in the susuki groups

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.Comment: submitte

On non-commuting sets and centralizers in infinite group

A subset X of a group G is a set of pairwise non-commuting ele- ments if ab 6= ba for any two distinct elements a and b in X. If jXj ? jY j for any other set of pairwise non-commuting elements Y in G, then X is said to be a maximal subset of pairwise non-commuting elements and the cardinality of such a subset is denoted by !(G). In this paper, among other thing, we prove that, for each positive integer n, there are only finitely many groups G, up to isoclinic, with !(G) = n (with exactly n centralizers).Comment: 5 pages, to appear, Group Theory, 201