  Let $(M,\omega)$ be a closed symplectic manifold and $\textup{Ham}(M,\omega)$
the group of Hamiltonian diffeomorphisms of $(M,\omega)$. Then the Seidel
homomorphism is a map from the fundamental group of $\textup{Ham}(M,\omega)$ to
the quantum homology ring $QH_*(M;\Lambda)$. Using this homomorphism we give a
sufficient condition for when a nontrivial loop $\psi$ in
$\textup{Ham}(M,\omega)$ determines a nontrivial loop $\psi\times\textup{id}_N$
in $\textup{Ham}(M\times N,\omega\oplus\eta)$, where $(N,\eta)$ is a closed
symplectic manifold such that $\pi_2(N)=0$.
