Factoring nonabelian finite groups into two subsets

A group G is said to be factorized into subsets A₁, A₂,..., A_s ⊆ G if every element g in G can be uniquely represented as g = g1g2... gs, where gi ∈ A_i, i = 1, 2,..., s. We consider the following conjecture: for every finite group G and every factorization n = ab of its order, there is a factorization G = AB with |A| = a and |B| = b. We show that a minimal counterexample to this conjecture must be a nonabelian simple group and prove the conjecture for every finite group the nonabelian composition factors of which have orders less than 10 000.