Products of subsets in an abelian group

Let G be an abelian group of order n (written multiplicatively), let g∈G and let d be an integer such that 1⩽d⩽n. The paper establishes bounds on the number of d-element subsets S of G such that ∏x∈S x=g. This work generalises the problem of finding bounds on the number of monic root-free polynomials of degree d over a finite field Fq with a specified constant term.