  The group-theoretical classification of states of identical particle pairs is
presented. Then obtained states are coupled with those of an antiparticle to
construct states of a three-particle system. Investigations are performed using
products of irreducible projective representations of the 2D translation group.
For a given BvK period N degeneracy of pair states is N, whereas three-particle
states are N^2-fold degenerated. It has to be underlined that the case of even
N is more complicated since pair states are labelled by four inequivalent
irreducible projective representations. The problem of symmetry properties with
respect to particles transposition is briefly discussed.
