  For a large prime $p$, a rational function $\psi \in F_p(X)$ over the finite
field $F_p$ of $p$ elements, and integers $u$ and $H\ge 1$, we obtain a lower
bound on the number consecutive values $\psi(x)$, $x = u+1, \ldots, u+H$ that
belong to a given multiplicative subgroup of $F_p^*$.
