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It is often stated that the removal of gas by ram-pressure stripping of a galaxy disc is not a common process in galaxy groups. In this study, with the aid of an observational classification of galaxies and a simple physical model, we show that this may not be true. We examined and identified 45 ram-pressure-stripped galaxy candidates from a sample of 1311 galaxy group members within 125 spectroscopically selected galaxy groups. Of these, 13 galaxies are the most secure candidates with multiple distinct features. These candidate ram-pressure-stripped galaxies have similar properties to those found in clusters – they occur at a range of stellar masses, are largely blue and star-forming, and have phase-space distributions consistent with being first infallers into their groups. The only stand-out feature of these candidates is they exist not in clusters, but in groups, with a median halo mass of 1013.5 M⊙. Although this may seem surprising, we employ an analytic model of the expected ram-pressure stripping force in groups and find that reasonable estimates of the relevant infall speeds and intragroup medium content would result in ram-pressure-stripped galaxies at these halo masses. Finally, given the considerable uncertainty on the lifetime of the ram-pressure phase, this physical mechanism could be the dominant quenching mechanism in galaxy groups, if our ram-pressure-stripped candidates can be confirmed. [ABSTRACT FROM AUTHOR]