Ablikim, M (reprint author), Inst High Energy Phys, Beijing 100049, Peoples R China.
With a sample of (225.2 +/- 2.8) x 10(6) J/psi events registered in the BESIII detector, J/psi -> gamma pi(+)pi(-)eta' is studied using two eta' decay modes: eta' -> pi(+)pi(-)eta and eta' -> gamma rho(0). The X(1835), which was previously observed by BESII, is confirmed with a statistical significance that is larger than 20 sigma. In addition, in the pi(+)pi(-)eta' invariant-mass spectrum, the X(2120) and the X(2370), are observed with statistical significances larger than 7.2 sigma and 6.4 sigma, respectively. For the X(1835), the angular distribution of the radiative photon is consistent with expectations for a pseudoscalar.