Factoring by Subsets of Cardinality Prime or Four

AbstractRédei′s theorem asserts that if a finite abelian group is a direct product of subsets of prime cardinality, then at least one of the factors is periodic. A theorem of A. D. Sands and S. Szabó states that if a finite elementary 2-group is factored into subsets of cardinality four, then at least one of the factors is periodic. As a common generalization of these results we prove that if a finite abelian group whose 2-component is elementary is factored into subsets whose cardinalities are of prime or four, then at least one of the factors must be periodic