  We considered the three jet production processes in the region of the
incident lepton, photon, quark or gluon fragmentation. The fourth jet is
created by the recoil proton. The kinematics of jet production is discussed in
jets production in the fragmentation region. The non-trivial relation between
the momenta of the recoil proton and the polar angle of its emission was
derived.
  Based on this formalism the differential cross sections of QCD processes $gp
\to (ggg) p; \,\,\,qp \to (q \bar{Q} Q) p; \,\,\, gp \to (g Q \bar{Q})p$ were
obtained, including the distribution on transverse momentum component of jets
fragments. It was shown that the role of the contribution of "non-Abelian"
nature may become dominant in a particular kinematics of the final particles.
The kinematics, in which the initial particle changes the direction of movement
to the opposite one, was considered in the case of heavy quark-antiquark pair
production.
  Different distributions, including spectral, azimuthal and polar angle
distribution on the fragments of jets can be arranged using our results. We
present besides the behavior of the ratio of non-Abelian contribution to the
cross section to the total contribution. We show that it dominates for large
values of the transverse momenta of jets component (gluons or quarks). Some
historical introduction to the cross-sections of peripheral processes,
including 2$\gamma$ creation mechanism production, including the result
Brodsky-Kinoshita-Terazawa, is given.
