On a theorem of Jordan
HTML articles powered by AMS MathViewer
- by Jean-Pierre Serre PDF
- Bull. Amer. Math. Soc. 40 (2003), 429-440
Abstract:
The theorem of Jordan which I want to discuss here dates from 1872. It is an elementary result on finite groups of permutations. I shall first present its translations in Number Theory and Topology.References
-
1 E. Artin, Über eine neue Art von L-Reihen, Hamb. Abh. 3 (1923), 89–108 (= Coll. Papers, 105–124).
- Nigel Boston, Walter Dabrowski, Tuval Foguel et al., The proportion of fixed-point-free elements of a transitive permutation group, Comm. Algebra 21 (1993), no. 9, 3259–3275. MR 1228762, DOI 10.1080/00927879308824728
- Tadasi Nakayama, On Frobeniusean algebras. I, Ann. of Math. (2) 40 (1939), 611–633. MR 16, DOI 10.2307/1968946
- Peter J. Cameron and Arjeh M. Cohen, On the number of fixed point free elements in a permutation group, Discrete Math. 106/107 (1992), 135–138. A collection of contributions in honour of Jack van Lint. MR 1181907, DOI 10.1016/0012-365X(92)90540-V
- Teresa Crespo, Galois representations, embedding problems and modular forms, Collect. Math. 48 (1997), no. 1-2, 63–83. Journées Arithmétiques (Barcelona, 1995). MR 1464017 6 F. G. Frobenius, Über die Congruenz nach einem aus zwei endlichen Gruppen gebildeten Doppelmodul, J. Crelle 101 (1887), 279–299 (= Ges. Abh., II, 304–330). 7 F. G. Frobenius, Über Beziehungen zwischen den Primidealen eines algebraischen Körpers und den Substitutionen seiner Gruppe, Sitz. Akad. Wiss. Berlin (1896), 689–703 (= Ges. Abh., II, 719–733). 8 F. G. Frobenius, Über auflösbare Gruppen IV, Sitz. Akad. Wiss. Berlin (1901), 1216–1230 (= Ges. Abh., III, 189–203). 9 C. Jordan, Recherches sur les substitutions, J. Liouville 17 (1872), 351–367 (= Oe. I. 52). 10 L. Kronecker, Über die Irreductibilität von Gleichungen, Sitz. Akad. Wiss. Berlin (1880), 155–162 (= Werke, II, 83–93).
- P. Stevenhagen and H. W. Lenstra Jr., Chebotarëv and his density theorem, Math. Intelligencer 18 (1996), no. 2, 26–37. MR 1395088, DOI 10.1007/BF03027290
- Jacques Martinet, Petits discriminants des corps de nombres, Number theory days, 1980 (Exeter, 1980) London Math. Soc. Lecture Note Ser., vol. 56, Cambridge Univ. Press, Cambridge-New York, 1982, pp. 151–193 (French). MR 697261
- R. W. K. Odoni, On the norms of algebraic integers, Mathematika 22 (1975), no. 1, 71–80. MR 424757, DOI 10.1112/S0025579300004514
- Michael Rubinstein and Peter Sarnak, Chebyshev’s bias, Experiment. Math. 3 (1994), no. 3, 173–197. MR 1329368, DOI 10.1080/10586458.1994.10504289
- Saunders MacLane and O. F. G. Schilling, Infinite number fields with Noether ideal theories, Amer. J. Math. 61 (1939), 771–782. MR 19, DOI 10.2307/2371335
- Jean-Pierre Serre, Divisibilité de certaines fonctions arithmétiques, Enseign. Math. (2) 22 (1976), no. 3-4, 227–260. MR 434996
- Wilhelm Wirtinger, Über eine Minimalaufgabe im Gebiete der analytischen Funktionen von mehreren Veränderlichen, Monatsh. Math. Phys. 47 (1939), 426–431 (German). MR 56, DOI 10.1007/BF01695512
- Jean-Pierre Serre, Quelques applications du théorème de densité de Chebotarev, Inst. Hautes Études Sci. Publ. Math. 54 (1981), 323–401 (French). MR 644559 19 N. Tschebotareff (Chebotarev), Die Bestimmung der Dichtigkeit einer Menge von Primzahlen, welche zu einer gegebenen Substitutionsklasse gehören, Math. Ann. 95 (1925), 191–228.
Additional Information
- Jean-Pierre Serre
- Affiliation: Collège de France, 3, Rue d’Ulm, Paris, France
- MR Author ID: 158970
- Email: serre@dmi.ens.fr
- Received by editor(s): March 1, 2003
- Published electronically: July 17, 2003
- Additional Notes: This text first appeared in Math Medley 29 (2002), 3–18. The writing was done with the help of Heng Huat Chan. ©2002 Singapore Mathematical Society. Reprinted with permission
- © Copyright 2002 Singapore Mathematical Society
- Journal: Bull. Amer. Math. Soc. 40 (2003), 429-440
- MSC (2000): Primary 06-XX, 11-XX, 11F11
- DOI: https://doi.org/10.1090/S0273-0979-03-00992-3
- MathSciNet review: 1997347