Available in electronic format
Available in print format
Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)
     

On a theorem of Jordan

Author(s): Jean-Pierre Serre
Journal: Bull. Amer. Math. Soc. 40 (2003), 429-440.
MSC (2000): Primary 06-XX, 11-XX, 11F11
Posted: July 17, 2003
Retrieve article in: PDF DVI PostScript

Abstract | References | Similar articles | Additional information

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).

2.
N. Boston, W. Dabrowski, T. Foguel, P. J. Gies, D. A. Jackson, J. Leavitt and D. T. Ose, The proportion of fixed-point-free elements of a transitive permutation group, Comm. Algebra 21 (1993), 3259-3275. MR 94e:20002

3.
W. Burnside, Theory of Groups of Finite Order, 2nd edition, Cambridge Univ. Press, 1911 (= Dover Publ., 1955). MR 16:1086c

4.
P. J. Cameron and A. M. Cohen, On the number of fixed point free elements in a permutation group, Discrete Math. 106/107 (1992), 135-138. MR 93f:20004

5.
T. Crespo, Galois representations, embedding problems and modular forms, Collectanea Math. 48 (1997), 63-83. MR 98j:11101

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).

11.
H. W. Lenstra, Jr., and P. Stevenhagen, Chebotarëv and his density theorem, Math. Intelligencer 18 (1996), 26-37. MR 97e:11144

12.
J. Martinet, Petits discriminants des corps de nombres, Journées arithmétiques 1980 (J. V. Armitage, ed.), Cambridge Univ. Press, Cambridge, 1982, pp. 151-193. MR 84g:12009

13.
R. W. K. Odoni, On the norms of algebraic integers, Mathematika 22 (1975), 71-80. MR 54:12715

14.
M. Rubinstein and P. Sarnak, Chebyshev's Bias, Experiment. Math. 3 (1994), 173-197. MR 96d:11099

15.
E. S. Selmer, On the irreducibility of certain trinomials, Math. Scand. 4 (1956), 287-302. MR 19:7f

16.
J-P. Serre, Divisibilité de certaines fonctions arithmétiques, L'Ens. Math. 22 (1976), 227-260 (= Oe. 108). MR 55:7958

17.
J-P. Serre, Modular forms of weight one and Galois representations, Algebraic Number Fields (A. Fröhlich, ed.), Acad. Press, London, 1977, pp. 193-268 (= Oe. 110). MR 56:8497

18.
J-P. Serre, Quelques applications du théorème de densité de Chebotarev, Publ. Math. I.H.E.S. 54 (1981), 123-201 (= Oe. 125). MR 83k:12011

19.
N. Tschebotareff (Chebotarev), Die Bestimmung der Dichtigkeit einer Menge von Primzahlen, welche zu einer gegebenen Substitutionsklasse gehören, Math. Ann. 95 (1925), 191-228.


Similar Articles:

Retrieve articles in Bulletin of the American Mathematical Society with MSC (2000): 06-XX, 11-XX, 11F11

Retrieve articles in all Journals with MSC (2000): 06-XX, 11-XX, 11F11


Additional Information:

Jean-Pierre Serre
Affiliation: Collège de France, 3, Rue d'Ulm, Paris, France
Email: serre@dmi.ens.fr

DOI: 10.1090/S0273-0979-03-00992-3
PII: S 0273-0979(03)00992-3
Received by editor(s): March 1, 2003
Posted: July 17, 2003
Additional Notes: This text first appeared in \emph{Math Medley} \textbf{29} (2002), 3--18. The writing was done with the help of Heng Huat Chan. \copyright 2002 Singapore Mathematical Society. Reprinted with permission
Copyright of article: Copyright 2002, Singapore Mathematical Society


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google