  This paper is the third of a series in which we investigate the
discrimination between Gaussian (G) and Non-Gaussian (NG) clusters, based on
the velocity distribution of the member galaxies. We study a sample of 177
groups from the Yang catalog in the redshift interval of 0.03 $\le$ z $\le$ 0.1
and masses $\ge$ 10$^{14} \rm M_{\odot}$. Examining the projected stellar mass
density distributions of G and NG groups we find strong evidence of a higher
infall rate in the outskirts of NG groups over the G ones. There is a 61\%
excess of faint galaxies in NGs when contrasted with G groups, when integrating
$\rm from ~ 0.8 ~to~ 2.0R/R_{200}$. The study of the Star Formation History
(SFH) of ellipticals and spirals in the three main regions of the Projected
Phase Space (PPS) reveals also that the star formation in faint spirals of NG
groups is significantly different from their counterpart in the G groups. The
assembled mass for Faint spirals varies from 59\% at 12.7 Gyr to 75\% at 8.0
Gyr, while in G systems this variation is from 82\% to 91\%. This finding may
also be interpreted as a higher infall rate of gas rich systems in NG groups.
This accretion process through the filaments, disturbing the velocity
distribution and modifying not only the stellar population of the incoming
galaxies but also their SFH, should be seriously considered in modelling galaxy
evolution.
