Factoring an Infinite Abelian Group by Subsets

Abstract

By a theorem of L. Redei if a finite abelian group is a direct product of its subsets such that each subset has a prime number of elements and contains the identity element of the group, then at least one of the factors must be a subgroup. The content of this paper is that this result holds for certain infinite abelian groups, too. Namely, for groups that are direct products of finitely many Pruferian groups and finite cyclic groups of prime power order, belonging to pairwise distinct primes.