Bose symmetry and threshold identities for the reaction. pi. N. --> pi pi. N

It is shown here that when the constraints imposed on the amplitude of the reaction ..pi..N..--> pi pi..N by the exact symmetries of strong interactions (isotopic invariance, P and C parity, and Bose symmetry) are taken into account, relations can be obtained between the values of the cross sections for various channels near threshold. Bose-symmetric kinematical variables convenient for the canonical decomposition of the amplitude are introduced.