  This review examines the relationship between black hole activity and
kinematic gas-star misalignment in brightest group galaxies (BGGs) with
different merger rates. The formation history of galaxy groups is assessed
through "age-dating" as an indicator of distinct major mergers involving the
BGG. BGGs within groups characterized by a higher frequency of major mergers
are more likely to host active SMBHs. A consistent correlation is identified
between the level of black hole activity, as indicated by the 1.4 GHz and 325
MHz radio emissions, and the degree of kinematic misalignment between the gas
and stellar components in BGGs. In dynamically fossil groups, where black hole
accretion rate is relatively ($\sim 1$ dex) lower due to the lack of recent (
$\leq 1$ Gyr) major mergers, there is reduced ($\sim$ 30\%) misalignment
between the gas and stellar components of BGGs compared to non-fossil groups.
Additionally, the study reveals that BGGs in non-fossil groups show higher
levels of star formation rate and increased occurrence of mergers, contributing
to observed color differences. Exploring the properties and dynamics of the gas
disc influenced by mechanical AGN feedback through hydrodynamic simulations
suggests that AGN wind-induced effects further lead to persistent gas
misalignment of the disk around the supermassive black hole.
