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Maximal sum-free sets in finite abelian groups, V

Published online by Cambridge University Press:  17 April 2009

H.P. Yap
H.P. Yap
Affiliation:
Department of Mathematics, University of Singapore, Singapore.
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Abstract

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Let λ(G) be the cardinality of a maximal sum-free set in a group G. Diananda and Yap conjectured that if G is abelian and if every prime divisor of |G| is congruent to 1 modulo 3, then λ(G) = |G|(n−1)/3n where n is the exponent of G. This conjecture has been proved to be true for elementary abelian p−groups by Rhemtulla and Street ana for groups by Yap. We now prove this conjecture for groups G = Zpq ⊕ Zp where p and q are distinct primes.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 13 , Issue 3 , December 1975 , pp. 337 - 342
Copyright
Copyright © Australian Mathematical Society 1975

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]Mann, Henry B., Addition theorems: The addition theorems of group theory and number theory (Interscience Tracts in Pure and Applied Mathematics, 18. John Wiley, New York, London, Sydney, 1965).Google Scholar
[3]Rhemtulla, A.M. and Street, Anne Penfold, “Maximal sum-free sets in finite abelian groups”, Bull. Austral. Math. Soc. 2 (1970), 289–297.CrossRefGoogle Scholar
[4]Yap, H.P., “Maximal sum-free sets in finite abelian groups IV”, Nanta Math. 5 (1972), no. 3, 70–75.Google Scholar
[5]Yap, H.P., “Maximal sum-free sets in finite abelian groups, III”, J. Number Theory 5 (1973), 293–300.CrossRefGoogle Scholar