The low redshift Universe (z<~0.5) is not a dull place. Processes leading to the suppression of star formation and morphological transformation are prevalent: this is particularly evident in the dramatic upturn in the fraction of S0-type galaxies in clusters. However, until now, the process and environment of formation has remained unidentified. We present a HST-based morphological analysis of galaxies in the redshift-space selected group and field environments at z~0.4. Groups contain a much higher fraction of S0s at fixed luminosity than the lower density field, with >99.999% confidence. Indeed the S0 fraction in groups is at least as high as in z~0.4 clusters and X-ray selected groups, which have more luminous Intra Group Medium (IGM). An 97% confident excess of S0s at >=0.3Mpc from the group centre at fixed luminosity, tells us that formation is not restricted to, and possibly even avoids, the group cores. Interactions with a bright X-ray emitting IGM cannot be important for the formation of the majority of S0s in the Universe. In contrast to S0s, the fraction of elliptical galaxies in groups at fixed luminosity is similar to the field, whilst the brightest ellipticals are strongly enhanced towards the group centres (>99.999% confidence within 0.3Mpc). We conclude that the group and sub-group environments must be dominant for the formation of S0 galaxies, and that minor mergers, galaxy harassment and tidal interactions are the most likely responsible mechanisms. This has implications not only for the inferred pre-processing of cluster galaxies, but also for the global morphological and star formation budget of galaxies: as hierarchical clustering progresses, more galaxies will be subject to these transformations as they enter the group environment.
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