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Maximal Sum-Free Sets in Elementary Abelian p-Groups

Published online by Cambridge University Press:  20 November 2018

A. H. Rhemtulla  and
Anne Penfold Street
A. H. Rhemtulla
Affiliation:
University of Alberta, Edmonton, Alberta
Anne Penfold Street
Affiliation:
University of Alberta, Edmonton, Alberta
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Given an additive group G and nonempty subsets S, T of G, let S+T denote the set ﹛s + t | s ∊ S, t ∊ T﹜, S the complement of S in G and |S| the cardinality of S. We call S a sum-free set in G if (S+S) ⊆ S. If, in addition, |S| ≥ |T| for every sum-free set T in G, then we call S a maximal sum-free set in G. We denote by λ(G) the cardinality of a maximal sum-free set in G.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 1 , January 1971 , pp. 73 - 80
Copyright
Copyright © Canadian Mathematical Society 1971

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. Mann, H. B., Addition theorems: The addition theorems of group theory and number theory, Interscience, New York, 1965.Google Scholar
3. Rhemtulla, A. H. and Street, A. P., Maximal sum-free sets in finite abelian groups, Bull. Austral. Math. Soc, 2 (1970), 289-297.Google Scholar