  In the Regge kinematics the amplitude for gluon production off three
scattering centers is found in the Lipatov effective action technique. The
vertex for gluon emission with the reggeon splitting in three reggeons is
calculated and its transversality is demonstrated. It is shown that in the sum
of all contributions terms containing principal value singularities are
cancelled and substituted by the standard Feynman poles. These results may be
used for calculation of the inclusive cross-section for gluon production on two
nucleons in the nucleus.
