Differential cross sections for the production of nuclear fragments at an angle of 3.5° in the fragmentation of 2-GeV/nucleon carbon ions on a beryllium target were measured in the FRAGM experiment performed at the ITEP-TWA heavy-ion accelerator-accumulator complex. The predictions of four Monte Carlo models of ion-ion interactions (BC, INCL, LAQGSM, and QMD) were tested on the basis of a comparison with the momentum spectra of fragments. Successes and drawbacks of these models are discussed. The energy spectra of protons and 3 He nuclei in the cumulative region in the projectile rest frame are well described by an exponential dependence, which make it possible to estimate temperature parameters of their emission source.