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We propose a theoretical approach to the consideration of the Hamiltonian with pairing forces using the technique of finite boson representation. We show that a simultaneous description of the pairing vibrational state in 56Ni and the pairing rotational states with the isospin T = 0 in the neighboring N = Z nuclei is possible if the pairing Hamiltonian takes into account only isovector monopole pairing. However, the calculated energies of the pairing rotational states of N = Z nuclei obtained from 56Ni by adding (removing) 12 or more nucleons exceed significantly the experimental values. A possible reason for this discrepancy is discussed.