  Understanding the interaction between galaxies and their surroundings is
central to building a coherent picture of galaxy evolution. Here we use GALEX
imaging of a statistically representative sample of 23 galaxy groups at z=0.06
to explore how local and global group environment affect the UV properties and
dust-corrected star formation rates of their member galaxies. The data provide
star formation rates out to beyond 2R_200 in all groups, down to a completeness
limit and limiting galaxy stellar mass of 0.06 M_sun/yr and 10^8 M_sun,
respectively. At fixed galaxy stellar mass, we find that the fraction of
star-forming group members is suppressed relative to the field out to an
average radius of R ~ 1.5 Mpc ~ 2R_200, mirroring results for massive clusters.
For the first time we also report a similar suppression of the specific star
formation rate within such galaxies, on average by 40% relative to the field,
thus directly revealing the impact of the group environment in quenching star
formation within infalling galaxies. At fixed galaxy density and stellar mass,
this suppression is stronger in more massive groups, implying that both local
and global group environment play a role in quenching. The results favor an
average quenching timescale of at least ~2 Gyr and strongly suggest that a
combination of tidal interactions and starvation is responsible. Despite their
past and ongoing quenching, galaxy groups with more than four members still
account for at least ~25% of the total UV output in the nearby universe.
