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