  In the paper, a new method determining the wave vector star channel in the
reciprocal lattice space of crystal in the light of the translational symmetry
breaking is proposed, and, in order to consider the phase transitions according
to the wave vector star channel, the conception of wave vector star channel
group is adopted. By this method, it is revealed that the phase transitions in
crystal are induced not by any arbitrary combinations of arms of the given
star, but by the selected combinations of arms which are satisfied by symmetry
of the parent phase. The wave vector star channel group is defined as the set
of elements of space group leaving the wave vector star channel invariant. We
show that the conception of wave vector star channel group can be efficiently
used in studying the translational symmetry breaking related to all the
Lifshitz wave vector stars of 230 space groups.
