To understand the role of the galaxy group environment on galaxy evolution,
we present a study of radio luminosity functions (RLFs) of group galaxies based
on the Karl G. Jansky Very Large Array-COSMOS 3 GHz Large Project. The
radio-selected sample of 7826 COSMOS galaxies with robust optical/near-infrared
counterparts, excellent photometric coverage, and the COSMOS X-ray galaxy
groups (M_200c > 10^13.3 M_0) enables us to construct the RLF of group galaxies
(GGs) and their contribution to the total RLF since z ~ 2.3. Using the Markov
chain Monte Carlo algorithm, we fit a redshift-dependent pure luminosity
evolution model and a linear and power-law model to the luminosity functions.
We compare it with past RLF studies from VLA-COSMOS on individual populations
of radio-selected star-forming galaxies (SFGs) and galaxies hosting active
galactic nuclei (AGN). These populations are classified based on the presence
or absence of a radio excess concerning the star-formation rates derived from
the infrared emission. We find that the fraction of radio group galaxies
evolves by a factor of ~ 3 from z ~ 2 to the present day. The increase in the
galaxy group contribution is due to the radio activity in groups being nearly
constant at z < 1, while it is declining in the field. We show that massive
galaxies inside galaxy groups remain radio active below redshift 1, contrary to
the ones in the field. This evolution in the GG RLF is driven mainly by
satellite galaxies in groups. Group galaxies associated with SFGs dominate the
GG RLF at z_med = 0.3, while at z_med = 0.8, the peak in the RLF, coinciding
with a known overdensity in COSMOS, is mainly driven by AGN. The study provides
an observational probe for the accuracy of the numerical predictions of the
radio emission in galaxies in a group environment.Comment: submitted to A&A; 15 pages, 6 figures, 8 table