  We calculate examples of Picard groups for 2-blocks with abelian defect
groups with respect to a complete discrete valuation ring. These include all
blocks with abelian 2-groups of 2-rank at most three with the exception of the
principal block of J1. In particular this shows directly that all such Picard
groups are finite and Picent, the group of Morita auto-equivalences fixing the
centre, is trivial. These are amongst the first calculations of this kind.
Further we prove some general results concerning Picard groups of blocks with
normal defect groups as well as some other cases.
