We explore the co-evolution of galaxies in nearby groups (V < 3000 km/s) with a multi-wavelength approach. We analyze GALEX far-UV (FUV) and near-UV (NUV) imaging and SDSS u,g,r,i,z data of groups spanning a large range of dynamical phases. We characterize the photometric properties of spectroscopically-confirmed galaxy members and investigate the global properties of the groups through a dynamical analysis. Here we focus on NGC 5846, the third most massive association of Early-Type Galaxies (ETG) after the Virgo and Fornax clusters. The group, composed of 90 members, is dominated by ETGs (about 80 per cent), and among ETGs about 40% are dwarfs. Results are compared with those obtained for three groups in the LeoII cloud, which are radically different both in member-galaxy population and dynamical properties. The FUV-NUV cumulative colour distribution and the normalized UV luminosity function (LF) significantly differ due to the different fraction of late-type galaxy population. The UV LF of NGC 5846 resembles that of the Virgo cluster, however our analysis suggests that star-formation episodes are still occurring in most of the group galaxies, including ETGs. The NUV-i colour distribution, the optical-UV colour-colour diagram, and NUV-r vs. Mr colour-magnitude relation suggest that the gas contribution cannot be neglected in the evolution of ETG-type group members. Our analysis highlights that NGC~5846 is still in an active phase of its evolution, notwithstanding the dominance of dwarf and bright ETGs and its virialized configuration.
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