Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-12-03T20:24:33.717Z Has data issue: false hasContentIssue false
  • English
  • Français

The theorem of Marggraff on primitive permutation groups which contain a cycle

Published online by Cambridge University Press:  17 April 2009

Richard Levingston  and
D.E. Taylor
Richard Levingston
Affiliation:
Department of Pure Mathematics, University of Sydney, Sydney, New South Wales.
D.E. Taylor
Affiliation:
Department of Pure Mathematics, University of Sydney, Sydney, New South Wales.
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 short elementary proof is given of the theorem of Marggraff which states that a primitive permutation group which contains a cycle fixing k points is (k+1)-fold transitive. It is then shown that the method of proof actually yields a generalization of Marggraff's theorem.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 15 , Issue 1 , August 1976 , pp. 125 - 128
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Hall, Marshall Jr., “Group theory and block designs”, Proc. Internat. Conf. Theory of Groups, Austral. Nat. Univ., Canberra, Aug., 1965, 115–114 (Gordon and Breach, New York, London, Paris, 1967).Google Scholar
[2]Kantor, W.M., “2-transitive designs”, Combinatorics. Part 3: Combinatorial, group theory, 44–97 (Proc. Adv. Study Institute Combinatorics, Breukelen, 1974. Mathematical Centre Tracts, 57. Mathematisch Centrum, Amsterdam, 1974).Google Scholar
[3]Marggraff, Bernhard, “Ueber primitive Gruppen mit transitiven Untergruppen geringeren Grades”, (Inaugural-Dissertation, Giessen, 1888; printed Berlin 1889).Google Scholar
[4]Veblen, Oswald and Young, John Wesley, Protective geometry, Vol. I (Ginn, Boston and London, 1910).Google Scholar
[5]Wielandt, Helmut, Finite permutation groups (Academic Press, New York, 1964).Google Scholar