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

Published online by Cambridge University Press:  17 April 2009

Anne Penfold Street
Anne Penfold Street
Affiliation:
Department of Mathematics, University of Queensland, St Lucia, Queensland.
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A subset S of an additive group G is called a maximal sum-free set in G if (S+S) nS = 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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 6 , Issue 3 , June 1972 , pp. 439 - 441
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Diananda, Palahenedi Hewage and Yap, Hian Poh, “Maximal sum-free sets of elements of finite groups”, Proc. Japan Acad. 45 (1969). 1–5.Google Scholar
[2]Kemperman, J.H.B., “On small sunsets in an abelian group”, Acta Math. 103 (1960), 63–88.CrossRefGoogle Scholar
[3]Yap, Hian-Poh, “Structure of maximal sum-free sets in groups of order 3p”, Proc. Japan Acad. 46 (1970), 758–762.CrossRefGoogle Scholar