  We consider, for infinite cardinals kappa and alpha <= kappa^+, the group
Pi(kappa,< alpha) of sequences of integers, of length kappa, with non-zero
entries in fewer than alpha positions. Our main result tells when Pi(kappa,<
alpha) can be embedded in Pi(lambda,< beta). The proof involves some
set-theoretic results, one about familes of finite sets and one about families
of ultrafilters.
