On the prospect of discovering `galaxy groups' through radio
  observations
  Observed steep mass scaling of radio power from the available high mass
clusters has ruled out the prospect of detection of 'galaxy groups'. But, the
available simulations and observations of thermal emissions show that the
groups are merger prone, thus non-virialised, indicating better visibility in
the radio waves. Detection of radio emissions from them would help us to
understand the scale-dependent particle acceleration mechanisms also groups can
be a unique laboratory to test the models of cosmic magnetism and canbe the
potential source of WHIMs. So, we have modelled radio emissions from the
simulated structures using {\sc{ENZO}}. We present a model for computing
magnetic field and for the first time, used the electron energy spectrum from
both the Fermi I (DSA) and Fermi II (TRA) mechanisms to compute radio
emissions. Computed radio power from more than 200 simulated objects, mass
ranging $\geq 10^{13}$ to $2\times 10^{15} M_{\odot}$ show a new mass scaling
of $M_{500} \propto P_{1.4\;GHz}^{2.17\pm 0.08}$ and a strong correlation scale
of $L_X \propto P_{1.4\;GHz}^{1.08\pm 0.05}$. Both magnetic field and radio
power are shown to have adequately replicated the available observations at
high mass, allowing us to extend the results to further smaller masses. We
report that groups below $10^{14}\;\rm{M_{\odot}}$ show the existence of 10s of
nano to a sub-$\mu$G magnetic field and about 10$^{19-23}$ W Hz$^{-1}$ of radio
power, much higher than what existing mass scaling predicts. We found that the
combined radio power from TRA and DSA electrons can only fit very well to all
the observed `radio halos'. Finally, we have implemented this model on a real
data set obtained from the Sloan Digital Sky Survey (SDSS). It predicts about
10s to 100s $\mu$Jy/(10$\arcsec$ beam) of radio flux in groups indicating their
detectability with existing and aplenty with the future radio telescopes.
