On the Dénes-Hermann Theorem: a Different Approach

L. Fuchs and S. Golomb considered the following problem. In a finite group G of order n, let p(G) denote the set of all elements expressible as a product g1 ⋯ gn, where {gi, ⋯, gn} = G. Does p(G) coincide with a coset of the commutator subgroup of G? Dénes and Hermann answered in the affirmative. The present paper introduces a different approach, providing a more elementary proof in the case in which n is odd