Remarks on a Zero-Sum Theorem

✍ Scribed by Yair Caro

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 330 KB
• Volume: 76
• Category: Article
• ISSN: 0097-3165
• DOI: 10.1006/jcta.1996.0108

✦ Synopsis

Recently the following theorem in combinatorial group theory has been proved: Let G be a finite abelian group and let A be a sequence of members of G such that |A| |G| +D(G)&1, where D(G) is the Davenport constant of G. Then A contains a subsequence B such that |B|= |G| and b # B b=0. We shall present a generalization of this theorem which contains information on the extremal cases and in particular allows us to deduce a short proof of the extremal cases in the Erdo s Ginzburg Ziv theorem. We also present, using the above-mentioned theorem, a proof that if G has rank k then |A| |G|(1+(k+1)Â2 k )&1 suffices to ensure a zero-sum subsequence on |G| terms.