  We present a pilot analysis of the influence of galaxy stellar mass and
cluster environment on the probability of slow rotation in 22 central galaxies
at mean redshift $z=0.07$. This includes new integral-field observations of 5
central galaxies selected from the Sloan Digital Sky Survey, observed with the
SPIRAL integral-field spectrograph on the Anglo-Australian Telescope. The
composite sample presented here spans a wide range of stellar masses,
$10.9<$log(M$_{*}/$M$_{\odot})<12.0$, and are embedded in halos ranging from
groups to clusters, $12.9<$log(M$_{200}/$M$_{\odot})<15.6$. We find a mean
probability of slow rotation in our sample of P(SR)$=54\pm7$percent. Our
results show an increasing probability of slow rotation in central galaxies
with increasing stellar mass. However, when we examine the dependence of slow
rotation on host cluster halo mass we do not see a significant relationship. We
also explore the influence of cluster dominance on slow rotation in central
galaxies. Clusters with low dominance are associated with dynamically younger
systems. We find that cluster dominance has no significant effect on the
probability of slow rotation in central galaxies. These results conflict with a
paradigm in which halo mass alone predetermines central galaxy properties.
