Hostname: page-component-74656f9884-8r8nv Total loading time: 0 Render date: 2026-11-09T00:45:27.443Z Has data issue: false hasContentIssue false
  • English
  • Français

On Transitive Permutation Groups

Published online by Cambridge University Press:  01 February 2010

John H. Conway ,
Alexander Hulpke  and
John McKay
John H. Conway
Affiliation:
Mathematics Department, Princeton University, Princeton, New Jersey, USA, conway@math.princeton.edu
Alexander Hulpke
Affiliation:
School of Mathematical and Computational Sciences, University of St. Andrews, St. Andrews, Fife KY16 9SS, Scotland, ahulpke@dcs.st-and.ac.uk
John McKay
Affiliation:
Departments of Computer Science and Mathematics, Centre Interuniversitaire en Calcul Mathématique Algébrique, Concordia University, Montréal, Canada H3G 1M8, mckay@cs.concordia.ca

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.

We assign names and new generators to the transitive groups of degree up to 15, reflecting their structure.

Information

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 1 , 1998 , pp. 1 - 8
Copyright
Copyright © London Mathematical Society 1998

References

1. Academie des sciences, ‘Grand prix de mathématiques’, C. R. Acad. Sci. Paris XLIV (1857), pp. 793–795.Google Scholar
2. Butler, Gregory and McKay, John, ‘The transitive groups of degree up to 11’, Comm. Algebra 11 (1983) 863–911.CrossRefGoogle Scholar
3. Burckhardt, Heinrich, ‘Endliche discrete Gruppen’’, Encyclopädie der mathematischen Wissenschaften I, erster Teil (eds Meyer, W. F., Teubner, B. G., Leipzig, 1898), pp. 208–226.Google Scholar
4. Butler, Greg[ory], ‘The transitive groups of degree fourteen and fifteen’, J. Symb. Comput. 16 (1993) 413–422.Google Scholar
5. Conway, J[ohn] H., Curtis, R[obert] T., Norton, S[imon] P., Parker, R[ichard] A. and Wilson, R[obert] A.. ATLAS of finite groups (Oxford University Press, 1985).Google Scholar
6. Cannon, J[ohn] and Playoust, C[atherine] Playoust, An introduction to Magma (School of Mathematics and Statistics, University of Sydney, 1993).Google Scholar
7. Hulpke, Alexander, Konstruktion transitiver Permutationsgruppen, PhD thesis, Rheinisch-Westfälische Technische Hochschule, Aachen, Germany, 1996. (Verlag der Augustinus Buchhandlung, Aachen, ISBN 3–86073–427–X).Google Scholar
8. Krasner, Marc and Kaloujnine, Leo [A.], ‘Produit complet des groupes de permutations et problème d'extension de groupes II’, Acta Sci. Math. (Szeged) 14 (1951) 39–66.Google Scholar
9. Kuhn, Harry W., ‘On imprimitive substitution groups’, Amer. J. Math. 26 (1904) 45–102.CrossRefGoogle Scholar
10. Miller, George A., ‘List of transitive substitution groups of degree twelve’, Quart. J. Pure Appl. Math. 28 (1896) 193–231. Errata: Quart. J. Pure Appl. Math., 29 (1898) 249.Google Scholar
11. Miller, George A., ‘On the transitive substitution groups of degree thirteen and fourteen’, Quart. J. Pure Appl. Math. 29 (1898) 224–249.Google Scholar
12. Miller, George A., ‘Historical note on the determination of all the permutation groups of low degree’, The Collected Works of George Abram Miller 1 (ed. Miller, George A., University of Illinois Press, 1935), pp. 1–9.Google Scholar
13. Remak, Robert ‘Über die Darstellung der endlichen Gruppen als Untergruppen direkter Produkte’, J. Reine Angew. Math 163 (1930) 1–44.Google Scholar
14. Royle, Gordon F., ‘The transitive groups of degree twelve’, J. Symb. Comput., 4 (1987) 255–268.CrossRefGoogle Scholar
15. Schönert, Martin et al. , GAP 3.4, patchlevel 3. (Lehrstuhl D für Mathematik, Rheinisch-Westfälische Technische Hochschule, Aachen, 1995).Google Scholar
16. Short, Mark W.. The primitive soluble permutation groups of degree less than 256, Lecture Notes in Mathematics 1519 (Springer, Heidelberg, 1992).CrossRefGoogle Scholar
Supplementary material: PDF

JCM 1 Conway et al Appendix A

Conway et al Appendix A

Download JCM 1 Conway et al Appendix A(PDF)
PDF 354.3 KB
Supplementary material: File

JCM 1 Conway et al Appendix B

Conway et al Appendix B

Download JCM 1 Conway et al Appendix B(File)
File 10.9 KB