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Archive for History of Exact Sciences

, Volume 12, Issue 3, pp 217–243 | Cite as

New light on Frobenius' creation of the theory of group characters

  • Thomas Hawkins
Article

Keywords

Group Character 
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Bibliography

  1. Cayley, A., 1858a. “A Memoir on the Theory of Matrices,” Phil. Trans. R. Soc. London. 148, 17–37.Google Scholar
  2. Cayley, A., 1858b. “A Memoir on the Automorphic Linear Transformation of a Bipartite Quadratic Function,” Phil. Trans. R. Soc. London, 148, 39–46.Google Scholar
  3. Dedekind, R., 1885. “Zur Theorie der aus n Haupteinheiten gebildeten complexen Grössen,” Göttingen Nachr., 1885, 141–159.Google Scholar
  4. Dedekind, R., 1898. “Ueber Gruppen deren sämtliche Theiler Normaltheiler sind,” Mathematische Annalen, 48, 548–561.Google Scholar
  5. Dedekind, R., 1931. Gesammelte mathematische Werke, v. 2, Braunschweig.Google Scholar
  6. Frobenius, G., 1870. De functionum analyticarum unis variabilis per series infinitas repraesentatione, Berlin. Reprinted in Frobenius [1968]. A version was published in German in 1871 (Frobenius [1968: v. 1, 35–64]).Google Scholar
  7. Frobenius, G., 1877. “Ueber das Pfaffsche Problem,” Jl. für Math. (Crelle), 82, 230–315.Google Scholar
  8. Frobenius, G., 1878. “Ueber lineare Substitutionen und bilineare Formen,” Jl. für Math. (Crelle), 84, 1–63.Google Scholar
  9. Frobenius, G., 1879a. “Theorie der linearen Formen mit ganzen Coefficienten,” Jl. für Math. (Crelle), 86, 146–208.Google Scholar
  10. Frobenius, G., 1879b. “Ueber Gruppen von vertauschbaren Elementen” (with L. Stickelberger), Jl. für Math. (Crelle), 86, 217–262.Google Scholar
  11. Frobenius, G., 1880. “Theorie der linearen Formen mit ganzen Coefficienten (Forts.),” Jl. für Math. (Crelle), 88, 96–116.Google Scholar
  12. Frobenius, G., 1884. “Ueber Thetafunctionen mehrere Variablen,” Jl. für Math. (Crelle), 96, 100–122.Google Scholar
  13. Frobenius, G., 1887a. “Neuer Beweis des Sylowschen Satzes,” Jl. für Math. (Crelle), 100, 179–181.Google Scholar
  14. Frobenius, G., 1887b. “Ueber die Congruenz nach einem aus zwei endlichen Gruppen gebildeten Doppelmodul,” Jl. für Math. (Crelle), 101, 273–299.Google Scholar
  15. Frobenius, G., 1893a. (Antrittsrede), S'ber. Akad. d. Wiss. Berlin, 1893, 368–370.Google Scholar
  16. Frobenius, G., 1893b. “Ueber auflösbare Gruppen“, S'ber. Akad. d. Wiss. Berlin, 1893, 337–345.Google Scholar
  17. Frobenius, G., 1893c. “Gedächtnisrede auf Leopold Kronecker,” Abh. Akad. d. Wiss. Berlin, 1893, 3–22.Google Scholar
  18. Frobenius, G., 1895. “Ueber endliche Gruppen”, S'ber. Akad. d. Wiss. Berlin, 1895, 81–112.Google Scholar
  19. Frobenius, G., 1896. “Ueber Beziehungen zwischen den Primidealen eines algebraischen Körpers und den Substitutionen seiner Gruppe,” S'ber. Akad. d. Wiss. Berlin, 1896, 689–703.Google Scholar
  20. Frobenius, G., 1896a. “Ueber vertauschbare Matrizen,” S'ber. Akad. d. Wiss. Berlin, 1896, 601–614.Google Scholar
  21. Frobenius, G., 1896b. “Ueber Gruppencharaktere,“ S'ber. Akad. d. Wiss. Berlin, 1896, 985–1021.Google Scholar
  22. Frobenius, G., 1896c. “Ueber die Primfactoren der Gruppendeterminante,” S'ber. Akad. d. Wiss. Berlin, 1896, 1343–1382.Google Scholar
  23. Frobenius, G., 1898. “Ueber Relationen zwischen den Charakteren einer Gruppe und denen ihrer Untergruppen,” S'ber. Akad. d. Wiss. Berlin, 1898, 501–515.Google Scholar
  24. Frobenius, G., 1899. “Ueber die Composition der Charaktere einer Gruppe,” S'ber. Akad. d. Wiss. Berlin, 1899, 330–339.Google Scholar
  25. Frobenius, G., 1900. “Ueber die Charaktere der symmetrischen Gruppe,” S'ber. Akad. d. Wiss. Berlin, 1900, 516–534.Google Scholar
  26. Frobenius, G. “Theorie der hypercomplexen Grössen,” S'ber. Akad. d. Wiss. Berlin, 1903, 504–537.Google Scholar
  27. Frobenius, G., 1968. Gesammelte Abhandlungen, 3 vols., Berlin.Google Scholar
  28. Hawkins, T., 1971. “The Origins of the Theory of Group Characters,” Archive Hist. Exact Sci., 7, 142–170.Google Scholar
  29. Hawkins, T., 1972. “Hypercomplex Numbers, Lie Groups, and the Creation of Group Representation Theory,” Archive Hist. Exact Sci., 8, 243–287.Google Scholar
  30. Kanunov, N. F., 1966. “O rabotakh F. E. Molina po teorii predstarlenii konechnykh grupp,” Istor-Mat. Issled., 17, 57–88.Google Scholar
  31. Kanunov, N. F., 1971. “Pisma G. Frobeniusa k F. E. Molina,” Istoriia i metodologiia estestvennykh nauk, 11, 56–68.Google Scholar
  32. Kimberling, C. H., 1972. “Emmy Noether,” Amer. Math. Mo., 79, 136–149.Google Scholar
  33. Kronecker, L., 1895. “Auszug aus einem Briefe von L. Kronecker an R. Dedekind,” S'ber. Akad. d. Wiss. Berlin, 1895, 115–117.Google Scholar
  34. Molien, T., 1898. “Ueber die Invarianten der linearen Substitutionsgruppen,” S'ber. Akad. d. Wiss. Berlin, 1897, 1152–1156.Google Scholar
  35. Siegel, C. L., 1968. “Erinnerungen an Frobenius,” Frobenius [1968], v. 1, pp. iv-vi.Google Scholar
  36. Wedderburn, J. H. M., 1905. “The Structure of Hypercomplex Number Systems” (with S. Epsteen), Trans. Amer. Math. Soc., 6, 172–178.Google Scholar
  37. Wedderburn, J. H. M., 1908. “Hypercomplex Numbers,” Proc. London Math. Soc, (2) 6, 77–118.Google Scholar

Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • Thomas Hawkins
    • 1
  1. 1.Department of MathematicsBoston UniversityUSA

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