Note on a Combinatorial Constant

Abstract:

      The following theorem is proved .Let G be a finite Abelian group,e the mximal order of an element in G,and a₁,…,a_D(G)+e-1 a sequence of D(G)+e-1 elements in G. Then, 0 can be written in the form 0=a_i1 +…+a_ie,with 1≤i₁<…< i_e ≤D(G) + e - 1.