  This paper studies the rainbow connection number of the power graph
$\Gamma_G$ of a finite group $G$. We determine the rainbow connection number of
$\Gamma_G$ if $G$ has maximal involutions or is nilpotent, and show that the
rainbow connection number of $\Gamma_G$ is at most three if $G$ has no maximal
involutions. The rainbow connection numbers of power graphs of some
nonnilpotent groups are also given.
