Factoring by Simulated Subsets Original Research Article

Suppose that the finite abelian group G is a direct product of the subsets A1,..., An such that for each i, there is a subgroup Hi of G with Ai = Hi ≤ Ai ∩ Hi + p − 2, where p is the least prime factor of G. A. D. Sands proved that then Ai = Hi for some i. We prove that the same conclusion holds if Hi = Ai ≤ Ai ∩ Hi + pi − 2 for each i, where pi is the least prime factor of Ai. As generalizations of earlier results we prove two similar results.