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 \approx 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 2 R _ { 200 } in all groups , down to a completeness limit and limiting galaxy stellar mass of 0.06 M _ { \odot } yr ^ { -1 } and 1 \times 10 ^ { 8 } M _ { \odot } , 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 \approx 1.5 Mpc \approx 2 R _ { 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 \gtrsim 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 \sim 25 % of the total UV output in the nearby universe .