  We study the radio and optical properties of the brightest group galaxies
(BGGs) in a sample of galaxy groups from the SDSS DR7. The luminosity
difference between the BGG and the second ranked galaxy in the group (known as
the luminosity, or magnitude, gap) has been used as a probe for the level of
galaxy interaction for the BGG within the group. We study the properties of
BGGs with magnitude gaps in the range 0-2.7 magnitudes, in order to investigate
any relation between luminosity gap and the radio properties of the BGG. In
order to eliminate selection biases, we ensure that all variations in stellar
mass are accounted for. We then confirm that, at fixed stellar mass, there are
no significant variations in the optical properties of the BGGs over the full
range of luminosity gaps studied. We compare these optical results with the
EAGLE hydrodynamical simulations and find broad consistency with the
observational data. Using EAGLE we also confirm that no trends begin to arise
in the simulated data at luminosity gaps beyond our observational limits.
Finally, we find that, at fixed stellar mass, the fraction of BGGs that are
radio-loud also shows no trends as a function of luminosity gap. We examine how
the BGG offset from the center of group may affect the radio results and find
no significant trend for the fraction of radio-loud BGGs with magnitude gap in
either the BGG samples with greater or less than 100kpc offset from the center
of group.

Astrophysics of Galaxies