Product representations of group elements
Dénes and Hermann proved that given a finite group G, exactly the elements of a suitable coset modulo the derived group of G can be represented as a product of \(| G|\) different elements of G. The aim of this paper is to prove that for \(j<| G|\) each element of G can be represented as a product of j different elements of G unless G is an elementary abelian 2-group, \(j=2\) or \(j=| G| -2\) in which case only the non-identity elements of G are representable as a product of j different elements.
scientific article; zbMATH DE number 4191986