DOI link for Various factorizations
Various factorizations book
In Section 5.1 here we consider the Re´dei property. If in a normalized factorization of an abelian group G = A+ B we have that 〈A〉 = H is a proper subgroup of G, then it is clear that A + (B ∩H) = H . Thus we have a factorization of a smaller group. We consider situations where this is useful, but we also give examples of factorizations which do not have this property, that is, where 〈A〉 = 〈B〉 = G. In Section 5.2 we consider quasi-periodic factorizations, which is a gener-
alization of the concept of periodic factorizations. When Hajo´s first found examples of non-periodic factorizations, he asked whether the factorizations must satisfy this weaker condition. We give examples to show that this need not be the case but also show that under certain conditions it will be so.