Remarks on Devenport′s Constant

Abstract:

      Let G be a finite group (written additively). The Davenport's constant D (G) is the minimal integer d such that, every sequence of d elements in G contains a nonempty subsequence such that the sum of whose elements in a suitable order is zero.In this paper, some estimations are proved on D (G). It is shown among other results that if G=H⊕Z_em and e=e(H) then D(G)≤em+e|H|-e, where H is a finite group,and e(H) is the least common mutiplier of orders of elements in H.