FACTORING BY SIMULATED SUBSETS

Suppose that the finite abelian group G is a direct product of the sub sets A(1),..., A(n) such that for each i, there is a subgroup H-i of G with /A(i)/ = /H-i/ less than or equal to /A(i) boolean AND H-i/ + p - 2, where p is the least prime factor of /G/. A. D. Sands proved that then A(i) = H-i for some i. We prove that the same conclusion holds i f /H-i/ = /A(i)/ less than or equal to /A(i) boolean AND H-i/ + p(i) - 2 for each i, where p(i) is the least prime factor of /A(i)/. As gene ralizations of earlier results we prove two similar results. (C) 1995 Academic Press, Inc.