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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.
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Abstract

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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

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