A Hajós-Keller type result on factorization of finite cyclic groups
Let G be a finite Abelian group, let \(g\in G\) and denote by [g,q] the simplex \(\{\) 0,g,2g,...,(q-1)g\(\}\), where \(1\leq q\leq | g|\). A normed factorization of G is an equality of the form \(G=A_ 1+A_ 2+...+A_ n\), where \(0\in A_ i\subset G\), \(1\leq i\leq n.\) Using Hajos' theorem, the authors prove the following result which is related to a conjecture of Keller [cf. \textit{S. K. Stein}, Am. Math. Mon. 81, 445-462 (1974; Zbl 0284.20048)]: If \(G=H+[g_ 1,q_ 1]+...+[g_ n,q_ n]\) is a normed factorization of the finite cyclic group G, then there exists some j, \(1\leq j\leq n\) such that \(q_ jg_ j\in <H>\).
scientific article; zbMATH DE number 4202587