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 $ome...