Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-27T23:34:28.334Z Has data issue: false hasContentIssue false
  • English
  • Français

An algebraic characterization of finite symmetric tournaments

Published online by Cambridge University Press:  17 April 2009

J.L. Berggren
J.L. Berggren
Affiliation:
Simon Fraser University, Burnaby, British Columbia, Canada.
Rights & Permissions [Opens in a new window]

Abstract

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.

A tournament T is called symmetric if its automorphism group is transitive on the points and arcs of T. The main result of this paper is that if T is a finite symmetric tournament then T is isomorphic to one of the quadratic residue tournaments formed on the points of a finite field GF(pn), pn ≡ 3 (4), by the following rule: If a, b ∈ GF(pn) then there is an are directed from a to b exactly when b – a is a non-zero quadratic residue in GF(pn).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 6 , Issue 1 , February 1972 , pp. 53 - 59
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Feit, Walter and Thompson, John G., “Solvability of groups of odd order”, Pacific J. Math. 13 (1963), 775–1029.CrossRefGoogle Scholar
[2]Goldberg, Myron, “The group of the quadratic residue tournament”, Canad. Math. Bull. 13 (1970), 51–54.CrossRefGoogle Scholar
[3]Huppert, B., Endliche Gruppen I (Die Grundlehren der mathematischen Wissenschaften, Band 134. Springer-Verlag, Berlin, Heidelberg, New York, 1967).CrossRefGoogle Scholar
[4]Passman, Donald, Permutation groups (W.A. Benjamin, New York, Amsterdam, 1968).Google Scholar