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We present the study of the south-west group in the Fornax cluster centred onthe brightest group galaxy (BGG) Fornax A, observed as part of the Fornax DeepSurvey (FDS). This includes the analysis of the bright group members (mB < 16mag) and the intra-group light (IGL). The main objective of this work is toinvestigate the assembly history of the Fornax A group and to compare itsphysical quantities as a function of the environment to that of the Fornaxcluster core. For all galaxies, we extract the azimuthally averaged surfacebrightness profiles in three optical bands (g, r, i) by modelling the galaxy'sisophotes. We derive their colour profiles and structural parameters in allrespective bands. The long integration time and large covered area of the FDSallow us to also estimate the amount of IGL. The majority of galaxies in theFornax A group are late-type galaxies (LTGs), spanning a range of stellar massof $8 < log (M_* M_{\odot}) < 10.5$. Six out of nine LTGs show a Type III(up-bending) break in their light profiles, which is either suggestive ofstrangulation halting star-formation in their outskirts or their HI-richnesscausing enhanced star-formation in their outer-discs. The estimated luminosityof the IGL is $6 \pm 2 \times 10^{10} L_{\odot}$ in g-band, which correspondsto about 16% of the total light in the group. The Fornax A group appears to bein an early stage of assembly with respect to the cluster core. The environmentof the Fornax A group is not as dense as that of the cluster core, with allgalaxies except the BGG showing similar morphology, comparable colours andstellar masses, and Type III disc-breaks, without any clear trend of theseproperties with group-centric distances. The main contribution to the IGL isfrom the minor merging in the outskirts of the BGG NGC1316 and, probably, thedisrupted dwarf galaxies close to the group centre.

The Fornax Deep Survey with VST. X. The assembly history of the bright galaxies and intra-group light in the Fornax A subgroup