Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-08T06:26:23.876Z Has data issue: false hasContentIssue false
  • English
  • Français

Complexes in Abelian Groups

Published online by Cambridge University Press:  20 November 2018

Peter Scherk  and
J. H. B. Kemperman
Peter Scherk
Affiliation:
University of Saskatchewan and University of Southern California
J. H. B. Kemperman
Affiliation:
Purdue University
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 an abelian group of order [G] ≤ ∞. Let A = {a}, B = {b}, … denote non-empty finite complexes in G. Let [A] be the number of elements of A. Finally put

A + B = {a + b}.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 6 , 1954 , pp. 230 - 237
Copyright
Copyright © Canadian Mathematical Society 1954

References

1. de Cauchy, A. L., Recherches sur tes nombres, Œuvres (2nd series, Paris, 1882), vol. 1, 39–63.Google Scholar
2. Chowla, I., A theorem on the addition of residue classes, Proc. Indian Acad. Sci., 2 (1935), 242–243.Google Scholar
3. Davenport, H., On the addition of residue classes, J. London Math. Soc, 10 (1935), 30–32.Google Scholar
4. Davenport, H., A historical note, J. London Math. Soc, 22 (1947), 100–101.Google Scholar
5. Hadwiger, H., Minkowskische Addition und Subtraktion beliebiger Punktmengen und die Theoreme von Erhard Schmidt, Math. Zeitschr., 53 (1950), 210–218.Google Scholar
6. Khintchine, A., Zur additiven Zahlentheorie, Matem. Sbornik, 39 (1932), 27–34.Google Scholar
7. Mann, H. B., On products of sets of group elements, Can. J. Math., 4 (1952), 64–66.Google Scholar
8. Shepherdson, J. C., On the addition of elements of a sequence, J. London Math. Soc, 22 (1947), 85–88.Google Scholar