The decay modes J/psi ->gamma pi(0), gamma eta and gamma eta(') are analyzed using a data sample of 58x10(6) J/psi decays collected with the BESII detector at the BEPC. The branching fractions are determined to be: Br(J/psi ->gamma pi(0))=(3.13(-0.47)(+0.65))x10(-5), Br(J/psi ->gamma eta)=(11.23 +/- 0.89)x10(-4), and Br(J/psi ->gamma eta('))=(5.55 +/- 0.44)x10(-3), where the errors are combined statistical and systematic errors. The ratio of partial widths Gamma(J/psi ->gamma eta('))/Gamma(J/psi ->gamma eta) is measured to be 4.94 +/- 0.40, and the singlet-octet pseudoscalar mixing angle of eta-eta(') system is determined.
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