Maximal sum-free sets in abelian groups of order divisible by three

Anne Street

Type: Article

Publication Date: 1972-06-01

Citations: 7

DOI: https://doi.org/10.1017/s0004972700044695

Abstract

A subset S of an additive group G is called a maximal sum-free set in G if ( S + S ) n S = Φ and | S | ≥ | T | for every sum-free set T in G . In this note, we prove a conjecture of Yap concerning the structure of maximal sum-free sets in finite abelian groups of order divisible by 3 but not divisible by any prime congruent to 2 modulo 3.

Locations

Bulletin of the Australian Mathematical Society - View - PDF

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+ PDF Chat	A new critical pair theorem applied to sum-free sets in Abelian groups	2004	Yahya Ould Hamidoune Alain Plagne
+	THE MAXIMUM SIZE OF -SUM-FREE SETS IN CYCLIC GROUPS	2018	Béla Bajnok Ryan Matzke
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+	The Maximum Size of $(k,l)$-Sum-Free Sets in Cyclic Groups	2018	Béla Bajnok Ryan Matzke
+	Additive Number Theory	2004	Richard K. Guy
+	Sum-free sets and sequences	1988	Cengiz Altay Ozgener

Works Cited by This (3)

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+ PDF Chat	Structure of maximal sum-free sets in groups of order $3p$	1970	Hian-Poh Yap
+ PDF Chat	Maximal sum-free sets of elements of finite groups	1969	P. H. Diananda Hian Poh Yap
+ PDF Chat	On small sumsets in an abelian group	1960	J. H. B. Kemperman