Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-26T05:55:11.438Z Has data issue: false hasContentIssue false
  • English
  • Français

Set-Transitive Permutation Groups

Published online by Cambridge University Press:  20 November 2018

R. A. Beaumont  and
R. P. Peterson
R. A. Beaumont
Affiliation:
University of Washington
R. P. Peterson
Affiliation:
University of Washington
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 concept of an s-ply transitive (1 ≤ s ≤ n) permutation group on n symbols is of considerable importance in the classical theory of finite permutation groups, which was in the height of its development in the period around the turn of the century. The obvious generalization to a permutation group which is s set-transitive (i.e., a group which, for each pair of s-element unordered subsets S, T of the given n symbols, contains a permutation which carries S into T) seems to have received little attention.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 7 , 1955 , pp. 35 - 42
Copyright
Copyright © Canadian Mathematical Society 1955

References

1. Bays, S., Sur la transitivité et la primitivité des groupes de substitutions, Comm. Math. Helvet, 22 (1949), 17–30.Google Scholar
2. Breusch, R., Zur Verallgemeinerung des Bertrandschen Postulates, das zwischen x und 2x stets Primzahlen liegen, Math. Zeitschrift, 34 (1932), 505–526.Google Scholar
3. Burnside, W., Theory of groups (Cambridge, 1897).Google Scholar
4. Burnside, W., Note on the simple group of order 504, Math. Ann., 52 (1899), 174–176.Google Scholar
5. Cole, F. N., Note on the substitution groups of six, seven, and eight letters, Bull. New York Math. Soc, 2 (1893), 184–190.Google Scholar
6. Cole, F. N., List of the substitution groups of nine letters, Quart. Jour. Math., 26 (1893), 372–388.Google Scholar
7. Miller, G. A., Collected works, vols. I and III (Urbana, 1935 and 1946).Google Scholar
8. von Neumann, J. and Morgenstern, O., Theory of games and economic behavior (Princeton, 1947).Google Scholar