  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.
