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On Transitive Permutation Groups

  • John H. Conway (a1), Alexander Hulpke (a2) and John McKay (a3)
Abstract

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

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References
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1. Academie des sciences, ‘Grand prix de mathématiques’, C. R. Acad. Sci. Paris XLIV (1857), pp. 793795.
2. Butler, Gregory and McKay, John, ‘The transitive groups of degree up to 11’, Comm. Algebra 11 (1983) 863911.
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.
4. Butler, Greg[ory], ‘The transitive groups of degree fourteen and fifteen’, J. Symb. Comput. 16 (1993) 413422.
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).
6. Cannon, J[ohn] and Playoust, C[atherine] Playoust, An introduction to Magma (School of Mathematics and Statistics, University of Sydney, 1993).
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).
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) 3966.
9. Kuhn, Harry W., ‘On imprimitive substitution groups’, Amer. J. Math. 26 (1904) 45102.
10. Miller, George A., ‘List of transitive substitution groups of degree twelve’, Quart. J. Pure Appl. Math. 28 (1896) 193231. Errata: Quart. J. Pure Appl. Math., 29 (1898) 249.
11. Miller, George A., ‘On the transitive substitution groups of degree thirteen and fourteen’, Quart. J. Pure Appl. Math. 29 (1898) 224249.
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.
13. Remak, Robert ‘Über die Darstellung der endlichen Gruppen als Untergruppen direkter Produkte’, J. Reine Angew. Math 163 (1930) 144.
14. Royle, Gordon F., ‘The transitive groups of degree twelve’, J. Symb. Comput., 4 (1987) 255268.
15. Schönert, Martin et al. , GAP 3.4, patchlevel 3. (Lehrstuhl D für Mathematik, Rheinisch-Westfälische Technische Hochschule, Aachen, 1995).
16. Short, Mark W.. The primitive soluble permutation groups of degree less than 256, Lecture Notes in Mathematics 1519 (Springer, Heidelberg, 1992).
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LMS Journal of Computation and Mathematics
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  • EISSN: 1461-1570
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