  A number is perfect if it is the sum of its proper divisors; here we call a
finite group `perfect' if its order is the sum of the orders of its proper
normal subgroups. (This conflicts with standard terminology but confusion
should not arise.) The notion of perfect group generalizes that of perfect
number, since a cyclic group is perfect exactly when its order is perfect. We
show that, in fact, the only abelian perfect groups are the cyclic ones, and
exhibit some non-abelian perfect groups of even order.
