  Let~$S$ be a finite nonabelian simple group, and let $H$ be a subgroup of
$S$. In this work, the dominion (in the sense of Isbell) of $H$ in $S$ in
rmVar(S)$ is determined, generalizing an example of B.H. Neumann. A necessary
and sufficient condition for $H$ to be epimorphically embedded in $S$ is
obtained. These results are then extended to a variety generated by a family of
finite nonabelian simple groups.
