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Maximal sum-free sets in cyclic groups of prime-power order
Published online by Cambridge University Press: 17 April 2009
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. In this paper, the maximal sum-free sets in cyclic p–groups are characterized to within automorphism.
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- 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), 1–5.Google Scholar
[2]Kemperman, J.H.B., “On small sumsets in an abelian group”, Acta Math. 103 (1960), 63–88.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), 289–297.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), 68–71.Google Scholar
[7]Yap, H.P., “Structure of maximal sum-free sets in C p”, Acta Arith. 17 (1970), 29–35.CrossRefGoogle Scholar