Measurements of the analysing power for the p(pol)p --> ppeta reaction have been performed in the close-to-threshold energy region at beam momenta of p_{beam}=2.010 and 2.085 GeV/c, corresponding to excess energies of Q=10 and 36 MeV, respectively. The determined analysing power is essentially consistent with zero implying that the eta meson is produced predominantly in the s-wave at both excess energies. The angular dependence of the analysing power, combined with the hitherto determined isospin dependence of the total cross section for the eta meson production in nucleon-nucleon collisions, reveal a statistically significant indication that the excitation of the nucleon to the S_{11}(1535) resonance, the process which intermediates the production of the eta meson, is predominantly due to the exchange of the pi meson between the colliding nucleons.
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