Simulated factorizations

AbstractFactoring a finite abelian group by its subsets is a direct product of these subsets giving the group. The paradigmatic problem of the theory of factorization is to describe conditions under which a subgroup must occur among the factors. Hajós' and Rédei's theorems give the most significant results providing constraints to the structure and the cardinality of the factors, respectively. In this paper we introduce a different type of condition. Namely we show that if the factors are constructed from subgroups by changing a few elements then a subgroup must occur among the factors and we prove an extension of Rédei's theorem