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History of Group Theory

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References

  1. R. G. Ayoub, Paolo Ruffini’s contributions to the quintic, Arch. Hist. Ex. Sc. 1980, 23: 253–277.

    Article  MATH  MathSciNet  Google Scholar 

  2. E. T. Bell, The Development of Mathematics, McGraw Hill, 1945.

    Google Scholar 

  3. G. Birkhoff, Current trends in algebra, Amer. Math. Monthly 1973, 80: 760–782 and 1974, 81: 746.

    Article  MATH  MathSciNet  Google Scholar 

  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. N. Bourbaki, Elements of the History of Mathematics, Springer-Verlag, 1994.

    Google Scholar 

  6. J. E. Burns, The foundation period in the history of group theory, Amer. Math. Monthly 1913, 20: 141–148.

    Article  MathSciNet  Google Scholar 

  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. 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.

    Article  MATH  MathSciNet  Google Scholar 

  9. J. Dieudonné (ed. ), Abré gé d’Histoire des Mathé matiques, 1700—1900, 2 vols. , Hermann, 1978.

    Google Scholar 

  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. C. H. Edwards, The Historical Development of the Calculus, Springer-Verlag, 1979.

    Google Scholar 

  12. H. M. Edwards, Galois Theory, Springer-Verlag, 1984.

    Google Scholar 

  13. A. Gallian, The search for fnite simple groups, Math. Magazine 1976, 49: 163–179.

    Article  MATH  MathSciNet  Google Scholar 

  14. D. Gorenstein, Finite Simple Groups: An Introduction to their Classification, Plenum Press, 1982.

    Google Scholar 

  15. D. Gorenstein, The Classi?cation of Finite Simple Groups, Plenum Press, 1983.

    Google Scholar 

  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.

    MathSciNet  Google Scholar 

  17. T. Hawkins, Hypercomplex numbers, Lie groups, and the creation of group representation theory, Arch. Hist. Ex. Sc. 1971/72, 8: 243–287.

    Article  MathSciNet  Google Scholar 

  18. T. Hawkins, The Erlanger Programm of Felix Klein: Reflections on its place in the history of mathematics, Hist. Math. 1984, 11: 442–470.

    Article  MATH  MathSciNet  Google Scholar 

  19. B. M. Kiernan, The development of Galois theory from Lagrange to Artin, Arch. Hist. Ex. Sc. 1971/72, 8: 40–154.

    Article  MathSciNet  Google Scholar 

  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. M. Kline, Mathematical Thought from Ancient to ModemTimes, Oxford Univ. Press, 1972.

    Google Scholar 

  22. D. R. Lichtenberg, The Emergence of Structure in Algebra, Doctoral Dissertation, Univ. of Wisconsin, 1966.

    Google Scholar 

  23. U. Merzbach, Quantity to Structure: Development of Modern Algebraic Concepts from Leibniz to Dedekind, Doctoral Dissertation, Harvard Univ. , 1964.

    Google Scholar 

  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. L. Novy, Origins of Modern Algebra, Noordhoff, 1973.

    Google Scholar 

  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. J. -A. de Séguier, Thé orie des Groupes Finis. Elements de la Thé orie des Groupes Abstraits, Gauthier-Villars, Paris, 1904.

    Google Scholar 

  28. L. A. Shemetkov, Two directions in the development of the theory of non-simple ?nite groups, Russ. Math. Surv. 1975, 30: 185–206.

    Article  MATH  Google Scholar 

  29. R. Silvestri, Simple groups of ?nite order in the nineteenth century, Arch. Hist. Ex. Sc. 1979, 20: 313–356.

    Article  MATH  MathSciNet  Google Scholar 

  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. B. L. Van der Waerden, Die Algebra seit Galois, Jahresbericht der Deutsch. Math. Ver. 1966, 68: 155–165.

    MATH  Google Scholar 

  32. W. C. Waterhouse, The early proofs of Sylow’s theorem, Arch. Hist. Ex. Sc. 1979/80, 21: 279–290.

    Article  MathSciNet  Google Scholar 

  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. A. Cayley, The theory of groups, Amer. Jour. Math. 1878, 1: 50–52.

    Article  MathSciNet  Google Scholar 

  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.

    Article  MATH  MathSciNet  Google Scholar 

  36. J. Nicholson, The development and understanding of the concept of quotient group, Hist. Math. 1993, 20: 68–88.

    Article  MathSciNet  Google Scholar 

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Kleiner, I. (2007). History of Group Theory. In: Kleiner, I. (eds) A History of Abstract Algebra. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4685-1_2

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