  We present the first results from the COLA (Compact Objects in Low-power AGN)
project which aims to determine the relationship between one facet of AGN
activity, the compact radio core, with star formation in the circumnuclear
region of the host galaxy. This will be accomplished by the comparison of the
multi-wavelength properties of a sample of AGN with compact radio cores to
those of a sample of AGN without compact cores and a matched sample of galaxies
without AGN.
  In this paper we discuss the selection criteria for our galaxy samples and
present the initial radio observations of the 107 Southern galaxies in our
sample. Low-resolution ATCA observations at 4.8, 2.5 and 1.4 GHz and high
resolution, single baseline snapshots at 2.3 GHz with the Australian LBA are
presented. We find that for the majority of the galaxies in our sample, the
radio luminosity is correlated with the FIR luminosity.
  Compact radio cores are detected in 9 galaxies. The majority (8/9) of these
galaxies exhibit a significant radio excess and 50% (7/14) of the galaxies
which lie above the radio-FIR correlation by more than 1 sigma have compact
radio cores. The emission from the cores is too weak to account for this radio
excess and there is no evidence that the radio luminosity of the compact cores
is correlated with the FIR galaxy luminosity.
  The galaxies with compact cores tend to be classified optically as AGN, with
two thirds (6/9) exhibiting Seyfert-like optical emission line ratios, and the
remaining galaxies classified either as composite objects (2/9) or starburst
(1/9). (Abridged)
