We present a study focusing on the nature of compact groups through the study of their elliptical galaxies. We determine central velocity dispersions (σo) for 18 bright elliptical galaxies located in the core of Hickson compact groups and a control sample of 12 bright bona fide ellipticals located in the field or very loose groups. Several tests are carried out to avoid systematic effects in σ measurements. We use these velocity dispersions to compare the position of 11 compact group galaxies in the Fundamental Plane to that of a large and homogeneous sample of elliptical galaxies (Burstein et al., 1987). We find that little or no significant difference exists, as far as the Fundamental Plane is concerned, between ellipticals in compact groups and their counterparts in other environments.