Ultrafilters and partial products of infinite cyclic groups

by Blass and Shelah. [BsSh:854]
Communications in Algebra, 2005
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.

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