Title: A Sufficient Condition for Nilpotency of the Nilpotent Residual of a Finite Group,
Abstract: Let $G$ be a finite group with the property that if $a,b$ are powers of
$\delta_1^*$-commutators such that $(|a|,|b|)=1$, then $|ab|=|a||b|$. We show
that $\gamma_{\infty}(G)$ is nilpotent.