  We report a measurement of the supernova (SN) rates (Ia and core-collapse) in
galaxy clusters based on the 136 SNe of the sample described in Cappellaro et
al. (1999) and Mannucci et al. (2005).
  Early-type cluster galaxies show a type Ia SN rate (0.066 SNuM) similar to
that obtained by Sharon et al. (2007) and more than 3 times larger than that in
field early-type galaxies (0.019 SNuM). This difference has a 98% statistical
confidence level. We examine many possible observational biases which could
affect the rate determination, and conclude that none of them is likely to
significantly alter the results. We investigate how the rate is related to
several properties of the parent galaxies, and find that cluster membership,
morphology and radio power all affect the SN rate, while galaxy mass has no
measurable effect. The increased rate may be due to galaxy interactions in
clusters, inducing either the formation of young stars or a different evolution
of the progenitor binary systems.
  We present the first measurement of the core-collapse SN rate in cluster
late-type galaxies, which turns out to be comparable to the rate in field
galaxies. This suggests that no large systematic difference in the initial mass
function exists between the two environments.
