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Maximal sum-free sets in abelian groups of order divisible by three: Corrigendum

Published online by Cambridge University Press:  17 April 2009

Anne Penfold Street
Anne Penfold Street
Affiliation:
Department of Mathematics, University of Queensland, St Lucia, Queensland.
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The last step of the proof in [2] was omitted. To complete the argument, we proceed in the following way. We had shown that H = H(S) = H(S+S) = H(S-S), that |S-S| = 2|S| - |H| and hence that in the factor group G* = G/H of order 3m, the maximal sum-free set S* = S/H and its set of differences S* - S* are aperiodic, with

so that

By (1) and Theorem 2.1 of [1], S* - S* is either quasiperiodic or in arithmetic progression.

Type
Corrigendum
Information
Bulletin of the Australian Mathematical Society , Volume 7 , Issue 2 , October 1972 , pp. 317 - 318
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Kemperman, J.H.B., “On small sumsets in an abelian group”, Acta Math. 103 (1960), 63–88.CrossRefGoogle Scholar
[2]Street, Anne Penfold, “Maximal sum-free sets in abelian groups of order divisible by three”, Bull. Austral. Math. Soc. 6 (1972), 439–441.CrossRefGoogle Scholar