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 $a$, $langle a, brangle notin mathcal{n}$. 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 $omega(mathcal{n}_{pgl(2,q)})$, 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 with $q$ elements, respectively.