Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-26T18:55:21.995Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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