Hostname: page-component-848d4c4894-4rdrl Total loading time: 0 Render date: 2024-06-27T17:59:16.305Z Has data issue: false hasContentIssue false

Maximal sum-free sets in cyclic groups of prime-power order

Published online by Cambridge University Press:  17 April 2009

Anne Penfold Street
Affiliation:
University of Queensland, St Lucia, Queens land.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A subset S of an additive group G is called a maximal sum-free set in G if (S+S) ∩ S = ø and |S| ≥ |T| for every sum-free set T in G. In this paper, the maximal sum-free sets in cyclic p–groups are characterized to within automorphism.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Diananda, Palahenedi Hewage and Yap, Hian Poh, “Maximal sum-free sets of elements of finite groups”, Proc. Japan Acad. 45 (1969), 15.Google Scholar
[2]Kemperman, J.H.B., “On small sumsets in an abelian group”, Acta Math. 103 (1960), 6388.CrossRefGoogle Scholar
[3]Mann, Henry B., Addition theorems: The addition theorems of group theory and number theory (Interscience Tracts in Pure and Applied Mathematics, number 18; John Wiley, New York, London, Sydney, 1965).Google Scholar
[4]Rhemtulla, A.H. and Street, Anne Penfold, “Maximal sum-free sets in finite abelian groups”, Bull. Austral. Math. Soc. 2 (1970), 289297.CrossRefGoogle Scholar
[5]Rhemtulla, A.H. and Street, Anne Penfold, “Maximal sum-free sets in elementary atelian p-groups”, Canad. Math. Bull, (to appear).Google Scholar
[6]Yap, H.P., “The number of maximal sum-free sets in C p”, Nanta Math. 2 (1968), 6871.Google Scholar
[7]Yap, H.P., “Structure of maximal sum-free sets in C p”, Acta Arith. 17 (1970), 2935.CrossRefGoogle Scholar