The primary cosmic rays particles with energies above 10**20 eV have been observed at many extensive air shower arrays since the beginning of observations over 40 years ago. The validity of measurements of signal s(600) used as energy estimation parameter at the Yakutsk array has been confirmed. Our calculations show that the width of the time pulses increases from nearly 100 ns at a distance of 100 m from the shower axis up to 4 - 5 $\mu$s at 1500 m. The calculated estimate of energy of extensive air shower is ~ 1.7 times smaller than the experimental estimate for the same value s(600). The pointing directions of extensive air showers observed at the Pierre Auger Observatory were fitted within +-3.1**o with positions of the nearby active galactic nuclei from the Veron-Cetty and P. Veron catalog. The cosmic ray luminosity of the active galactic nuclei which happened to be a source of the particular cosmic ray event constitutes a fraction ~10**-4 of the optical one if only cosmic ray particles with energies above 6*10**19 eV are produced. If produced cosmic ray particles have a spectrum up to ~ 100 GeV then the cosmic ray luminosity of the active galactic nuclei should be much higher than the optical one.