FACTORING BY SUBSETS OF CARDINALITY PRIME OR 4

Redei's theorem asserts that if a finite abelian group is a direct pro duct of subsets of prime cardinality, then at least one of the factors is periodic. A theorem of A. D. Sands and S. Szabo states that if a f inite elementary 2-group is factored into subsets of cardinality four, then at least one of the factors is periodic. As a common generalizat ion of these results we prove that if a finite abelian group whose 2-c omponent is elementary is factored into subsets whose cardinalities ar e of prime or four, then at least one of the factors must be periodic. (C) 1994 Academic Press, Inc.