Nonnilpotent subsets in the Suzuki groups

Let G be a group and \mathcal{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, \langle a, b\rangle \not\in \mathcal{N}. If, for any other nonnilpotent subset B in G, |A|\geq |B|, then A is said to be a maximal nonnilpotent subset and the cardinality of this subset (if it exists) is denoted by \omega(\mathcal{N}_G). In this paper, among other results, we obtain \omega(\mathcal{N}_{Suz(q)}) and \omega(\mathcal{N}_{PGL(۲,q)}), where Suz(q) is the Suzuki simple group over the field with q elements and PGL(۲,q) is the projective general linear group of degree ۲ over the finite field with q elements, respectively.

Keywords:

Nilpotentlizer , Hypercenter of a group , Clique number , Graphs associated to groups