Three-fold Restricted Set Addition in Groups

✍ Scribed by Vsevolod F. Lev

• Book ID: 102570957
• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 63 KB
• Volume: 23
• Category: Article
• ISSN: 0195-6698
• DOI: 10.1006/eujc.2002.0584

✦ Synopsis

Let G be a finite abelian group with a 'sufficiently small' proportion of elements of order two. We prove that for any subset A ⊆ G of cardinality |A| > 5 13 |G| and any group element g ∈ G, there exist pairwise distinct a 1 , a 2 , a 3 ∈ A such that a 1 + a 2 + a 3 = g -unless A is contained in a coset of an index two subgroup or in a union of two cosets of an index five subgroup.

As an immediate corollary our result implies a recent conjecture of Gallardo et al. who addressed the group G = Z n with n odd and sets of cardinality |A| > 2 5 n.