In vacuum with an induced by strong electromagnetic wave refraction index larger than unity, an ultra-relativistic electron emits Cherenkov radiation. During the interaction with this wave the electron also radiates photons via the Compton scattering. Synergic Cherenkov-Compton process can be observed by colliding laser accelerated electrons with a high intensity electromagnetic pulse. Extremely high energy photons cannot be emitted via the Cherenkov radiation because the vacuum refraction index tends to unity at these energies. Experiments on studying these phenomena will reveal the properties of vacuum predicted by nonlinear quantum electrodynamics.

5 pages, 1 figure