Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-28T21:49:39.679Z Has data issue: false hasContentIssue false
  • English
  • Français

Maximal sum-free sets in finite abelian groups

Published online by Cambridge University Press:  17 April 2009

A. H. Rhemtulla  and
Anne Penfold Street
A. H. Rhemtulla
Affiliation:
The University of Alberta, Edmonton, Alberta, Canada.
Anne Penfold Street
Affiliation:
The University of Alberta, Edmonton, Alberta, Canada.
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. It is shown that if G is an elementary abelian p–group of order pn, where p = 3k ± 1, then a maximal sum-free set in G has kpn-1 elements. The maximal sum-free sets in Zp are characterized to within automorphism.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 2 , Issue 3 , June 1970 , pp. 289 - 297
Copyright
Copyright © Australian Mathematical Society 1970

References

[1]Diananda, P.H. and Yap, H.P., “Maximal sum-free sets of elements of finite groups”, Proc. Japan Acad. 45 (1969), 1–5.Google Scholar
[2]Erdös, P., “Extremal problems in number theory”, Proc. Sympos. Pure Math. 8, 181–189. (Amer. Math. Soc., Providence. R. T., 1965).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 & Sons, New York, London, Sydney, 1965).Google Scholar
[4]Vosper, A.G., “The critical pairs of subsets of a group of prime order”, J. London Math. Soc. 31 (1956), 200–205.CrossRefGoogle Scholar
[5]Vosper, A.G., “Addendum to ‘The critical pairs of subsets of a group of prime order’”, J. London Math. Soc. 31 (1956), 280–282.CrossRefGoogle Scholar
[6]Yap, H.P., “The number of maximal sum-free sets in Cp”, Nanta Math. 2 (1968), 68–71.Google Scholar