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We investigate the differences in the stellar population properties, the structure, and the environment between massive compact star-forming galaxies (cSFGs) with or without active galactic nucleus (AGN) at 2 < z < 3 in the five 3D-Hubble Space Telescope/CANDELS fields. In a sample of 221 massive cSFGs, we constitute the most complete AGN census so far, identifying 66 AGNs by the X-ray detection, the mid-infrared color criterion, and/or the spectral energy distribution fitting, while the rest (155) are non-AGNs. Further dividing these cSFGs into two redshift bins, i.e., 2 < z < 2.5 and 2.5 ≤ z < 3, we find that in each redshift bin the cSFGs with AGNs have similar distributions of the stellar mass, the specific star formation rate, and the ratio of LIR to LUV to those without AGNs. After having performed a two-dimensional surface brightness modeling for those cSFGs with X-ray-detected AGNs (37) to correct for the influence of the central point-like X-ray AGN on measuring the structural parameters of its host galaxy, we find that in each redshift bin the cSFGs with AGNs have comparable distributions of all concerned structural parameters, i.e., the Sérsic index, the 20%-light radius, the Gini coefficient, and the concentration index, to those without AGNs. With a gradual consumption of available gas and dust, the structure of cSFGs, indicated by the above structural parameters, seem to be slightly more concentrated with decreasing redshift. At 2 < z < 3, the similar environment between cSFGs with and without AGNs suggests that their AGN activities are potentially triggered by internal secular processes, such as gravitational instabilities or/and dynamical friction. [ABSTRACT FROM AUTHOR]