  Aims. We explore galaxies with ringed structures inhabiting poor and rich
groups with the aim of assessing the effects of local density environments on
ringed galaxy properties. Methods. We identified galaxies with inner, outer,
nuclear, inner+outer (inner and outer rings combined), and partial rings that
reside in groups by cross-correlating a sample of ringed galaxies with a group
catalog obtained from Sloan Digital Sky Survey (SDSS). The resulting sample was
divided based on group richness. To quantify the effects of rings and the role
of local density environment on galaxy properties, we constructed a suitable
control sample for each catalog of ringed galaxies, consisting of non-ringed
galaxies with similar values for the z, magnitude, morphology, group masses,
and environmental density distributions as those of ringed ones. We explored
the occurrence of ringed galaxies in poor and rich groups and analyzed several
galaxy properties, such as SFR, stellar populations, and colors. Results. We
obtained a sample of 637 ringed galaxies residing in groups. With 76% of these
galaxies inhabiting poor groups and 24% rich groups. In addition, ringed
galaxies in groups display a reduction in their star formation activity and
aged stellar populations, compared to non-ringed ones in the control samples.
However, the SFR is higher for nuclear rings in poor groups than for other
types. This disparity may stem from the environmental influence on the internal
processes of galaxies, either enhancing or diminishing star formation. Ringed
galaxies also show an excess of red colors and tend to populate the green
valley and the red sequence of color-magnitude and color-color diagrams, with a
surplus of galaxies in the red sequence, while non-ringed galaxies are found in
the green valley and the blue region. These trends are more significant in
galaxies with ringed structures residing in rich groups.
