Hostname: page-component-7479d7b7d-pfhbr Total loading time: 0 Render date: 2024-07-13T21:44:08.955Z Has data issue: false hasContentIssue false
  • English
  • Français

Solution to a problem of A. D. Sands

Published online by Cambridge University Press:  18 May 2009

Owen H. Fraser  and
Basil Gordon
Owen H. Fraser
Affiliation:
Los Angeles Valley College, University of California, Los Angeles
Basil Gordon
Affiliation:
Los Angeles Valley College, University of California, Los Angeles
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.

Let G be a finite additive abelian group, and suppose that A and B are subsets of G. We say that G = A⊕B if every element g ∈ G can be uniquely written in the form g = a + b, where a ∈ A, b ∈ B. The study of such decompositions (usually called factorizations in the literature) was initiated by G. Hájos [3] in connection with his solution to a problem of Minkowski in the geometry of numbers.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 20 , Issue 2 , July 1979 , pp. 115 - 117
Copyright
Copyright © Glasgow Mathematical Journal Trust 1979

References

REFERENCES

1.Fraser, O. and Gordon, B., Solution to a problem of L. Fuchs, Quart. J. Math. Oxford Set. 25 (1974), 1–8.CrossRefGoogle Scholar
2.Fuchs, L., Abelian Groups, 3rd edition (Pergamon, 1960), 331.Google Scholar
3.Hájos, G., Über einfache und mehrfache Bedeckung des n-dimensionalen Raumes mit einem Würfelgitter, Math. Z. 47 (1941), 427–467.CrossRefGoogle Scholar
4.Sands, A. D., On a problem of L. Fuchs, J. London Math. Soc. 37 (1962), 277–284.CrossRefGoogle Scholar
5.Sands, A. D., The factorization of abelian groups, Quart. J. Math. Oxford Ser. 10 (1959), 81–91.CrossRefGoogle Scholar
6.Sands, A. D., On the factorization of finite abelian groups II, Acta Math. Acad. Sci. Hungar. 13 (1962), 153–169.CrossRefGoogle Scholar
7.Sands, A. D., On a conjecture of G. Hájos, Glasgow Math. J. 15 (1974), 88–89.CrossRefGoogle Scholar
8.Swenson, C., Direct sum subset decomposition of abelian groups, Thesis, Washington State University (1972).Google Scholar
9.van Lint, J. H., Coding Theory (Springer, 1971), 85–91.CrossRefGoogle Scholar
10.van Lint, J. H., Survey of perfect codes, Rocky Mountain J. Math. 5 (1975), 199–220.Google Scholar