History of Group Theory

  • Israel Kleiner


Abelian Group Group Theory Simple Group Permutation Group Quotient Group 
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  1. 1.
    R. G. Ayoub, Paolo Ruffini’s contributions to the quintic, Arch. Hist. Ex. Sc. 1980, 23: 253–277.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    E. T. Bell, The Development of Mathematics, McGraw Hill, 1945.Google Scholar
  3. 3.
    G. Birkhoff, Current trends in algebra, Amer. Math. Monthly 1973, 80: 760–782 and 1974, 81: 746.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    G. Birkhoff, The rise of modern algebra to 1936, in Men and Institutions in American Mathematics, ed. by D. Tarwater, I. T. White, and I. D. Miller, Texas Tech. Press, 1976, pp. 41–63.Google Scholar
  5. 5.
    N. Bourbaki, Elements of the History of Mathematics, Springer-Verlag, 1994.Google Scholar
  6. 6.
    J. E. Burns, The foundation period in the history of group theory, Amer. Math. Monthly 1913, 20: 141–148.CrossRefMathSciNetGoogle Scholar
  7. 7.
    B. Chandler and W. Magnus, The History of Combinatorial Group Theory: A Case Study in the History of Ideas, Springer-Verlag, 1982.Google Scholar
  8. 8.
    A. Dahan, Les travaux de Cauchy sur les substitutions. Etude de son approche du concept de groupe, Arch. Hist. Ex. Sc. 1980, 23: 279–319.MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    J. Dieudonné (ed. ), Abré gé d’Histoire des Mathé matiques, 1700—1900, 2 vols. , Hermann, 1978.Google Scholar
  10. 10.
    P. Dubreil, L’algè bre, en France, de 1900 a 1935, Cahiers du seminaire d’histoire des mathé matiques 1981, 3: 69–81.Google Scholar
  11. 11.
    C. H. Edwards, The Historical Development of the Calculus, Springer-Verlag, 1979.Google Scholar
  12. 12.
    H. M. Edwards, Galois Theory, Springer-Verlag, 1984.Google Scholar
  13. 13.
    A. Gallian, The search for fnite simple groups, Math. Magazine 1976, 49: 163–179.MATHMathSciNetCrossRefGoogle Scholar
  14. 14.
    D. Gorenstein, Finite Simple Groups: An Introduction to their Classification, Plenum Press, 1982.Google Scholar
  15. 15.
    D. Gorenstein, The Classi?cation of Finite Simple Groups, Plenum Press, 1983.Google Scholar
  16. 16.
    R. R. Hamburg, The theory of equations in the 18th century: The work of Joseph Lagrange, Arch. Hist. Ex. Sc.. 1976/77, 16: 17–36.MathSciNetGoogle Scholar
  17. 17.
    T. Hawkins, Hypercomplex numbers, Lie groups, and the creation of group representation theory, Arch. Hist. Ex. Sc. 1971/72, 8: 243–287.CrossRefMathSciNetGoogle Scholar
  18. 18.
    T. Hawkins, The Erlanger Programm of Felix Klein: Reflections on its place in the history of mathematics, Hist. Math. 1984, 11: 442–470.MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    B. M. Kiernan, The development of Galois theory from Lagrange to Artin, Arch. Hist. Ex. Sc. 1971/72, 8: 40–154.CrossRefMathSciNetGoogle Scholar
  20. 20.
    F. Klein, Development of Mathematics in the 19th Century (transl. from the 1928 German ed. by M. Ackerman), in Lie Groups: History, Frontiers and Applications, vol. IX, ed. by R. Hermann, Math. Sci. Press, 1979, pp. 1–361.Google Scholar
  21. 21.
    M. Kline, Mathematical Thought from Ancient to ModemTimes, Oxford Univ. Press, 1972.Google Scholar
  22. 22.
    D. R. Lichtenberg, The Emergence of Structure in Algebra, Doctoral Dissertation, Univ. of Wisconsin, 1966.Google Scholar
  23. 23.
    U. Merzbach, Quantity to Structure: Development of Modern Algebraic Concepts from Leibniz to Dedekind, Doctoral Dissertation, Harvard Univ. , 1964.Google Scholar
  24. 24.
    G. A. Miller, History of the Theory of Groups, Collected Works, 3 vols. , pp. 427–467, pp. 1–18, and pp. 1–15, respectively, Univ. of Illinois Press, 1935, 1938, and 1946.Google Scholar
  25. 25.
    L. Novy, Origins of Modern Algebra, Noordhoff, 1973.Google Scholar
  26. 26.
    26. O. J. Schmidt, Abstract Theory of Groups, W. H. Freeman & Co. , 1966. (Translation by F. Holling and I. B. Roberts of the 1916 Russian edition. )Google Scholar
  27. 27.
    J. -A. de Séguier, Thé orie des Groupes Finis. Elements de la Thé orie des Groupes Abstraits, Gauthier-Villars, Paris, 1904.Google Scholar
  28. 28.
    L. A. Shemetkov, Two directions in the development of the theory of non-simple ?nite groups, Russ. Math. Surv. 1975, 30: 185–206.MATHCrossRefGoogle Scholar
  29. 29.
    R. Silvestri, Simple groups of ?nite order in the nineteenth century, Arch. Hist. Ex. Sc. 1979, 20: 313–356.MATHCrossRefMathSciNetGoogle Scholar
  30. 30.
    J. Tarwater, J. T. White, C. Hall, and M. E. Moore (eds. ), American Mathematical Heritage: Algebra and Applied Mathematics, Texas Tech. Press, 1981. Has articles by Feit, Fuchs, and MacLane on the history of finite groups, abelian groups, and abstract algebra, respectively.Google Scholar
  31. 31.
    B. L. Van der Waerden, Die Algebra seit Galois, Jahresbericht der Deutsch. Math. Ver. 1966, 68: 155–165.MATHGoogle Scholar
  32. 32.
    W. C. Waterhouse, The early proofs of Sylow’s theorem, Arch. Hist. Ex. Sc. 1979/80, 21: 279–290.CrossRefMathSciNetGoogle Scholar
  33. 33.
    H. Wussing, The Genesis of the Abstract Group Concept, M. I. T. Press, 1984. (Translation by A. Shenitzer of the 1969 German edition.)Google Scholar
  34. 34.
    A. Cayley, The theory of groups, Amer. Jour. Math. 1878, 1: 50–52.CrossRefMathSciNetGoogle Scholar
  35. 35.
    P. M. Neumann, What groups were: a study of the development of the axiomatics of group theory, Bull. Austral. Math. Soc. 1999, 60: 285–301.MATHMathSciNetCrossRefGoogle Scholar
  36. 36.
    J. Nicholson, The development and understanding of the concept of quotient group, Hist. Math. 1993, 20: 68–88.CrossRefMathSciNetGoogle Scholar

Copyright information

© Birkhäuser Boston 2007

Authors and Affiliations

  • Israel Kleiner
    • 1
  1. 1.Department of Mathematics and StatisticsYork UniversityTorontoCanada

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