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Bibliography
Artin, E., “The orders of the classical simple groups,” Comm. Pure Appl. Math. 8 (1955), 455–472.
Bell, E. T., “Fifty years of algebra in America 1888–1938,” Semicentennial Addresses of the American Mathematical Society (1938), 1–34.
Brahana, H. R., “George Abram Miller 1863–1951,” Bull. Amer. Math. Soc. 57 (1951), 377–382.
Burkhardt, H., “Untersuchungen aus dem Gebiete der hyperelliptischen Modulfunctionen II,” Math. Ann. 38 (1891), 161–224.
Burkhardt, H., “Untersuchungen aus dem Gebiete der hyperelliptischen Modulfunctionen III,” Math. Ann. 41 (1893), 313–343.
Burnside, W., “Notes on the theory of groups of finite order,” Proc. London Math. Soc. 25 (1893), 9–18.
Burnside, W., “On a class of groups defined by congruences,” Proc. London Math. Soc. 25 (1894), 113–139.
Burnside, W., “On a class of groups defined by congruences,” (second paper), Proc. London Math. Soc. 26 (1895), 58–106.
Burnside, W., “Notes on the theory of groups of finite order,” Proc. London Math. Soc. 26 (1895), 191–214, 325–338.
Burnside, W., Theory of Groups of Finite Order, University Press, Cambridge, 1897.
Burnside, W., Theory of Groups of Finite Order, second edition, University Press, Cambridge, 1911.
Cauchy, A., Œuvres Complètes, 26 volumes, Gauthier-Villars, Paris, 1882–1938.
Cayley, A., Collected Mathematical Papers, 14 volumes, University Press, Cambridge, 1889–1898.
Cole, F. N., “A contribution to the theory of the general equation of the sixth degree,” Amer. J. Math. 8 (1886), 265–286.
Cole, F. N., “Klein's Ikosaeder,” Amer. J. Math. 9 (1887), 45–61.
Cole, F. N., “Simple groups from order 201 to order 500,” Amer. J. Math. 14 (1892), 378–388.
Cole, F. N., “Simple groups as far as order 660,” Amer. J. Math. 15 (1893), 305–315.
Cole, F. N., “List of the transitive substitution groups of ten and eleven letters,” Quart. J. Math. 27 (1894), 39–50.
Cole, F. N., “On simple groups of low order,” Bull. Amer. Math. Soc. 30 (1924), 489–492.
Davis, C., A Bibliographical Survey of Simple Groups of Finite Order, 1900–1965, New York University, New York, 1969.
Dickson, L. E., Linear Groups with an Exposition of the Galois Field Theory, Dover, New York, 1958.
Dieudonné, J., “On the automorphisms of the classical groups” with a supplement by Loo-Keng Hua, Mem. Amer. Math. Soc. No. 2 (1951), vi+122 pp.
Dieudonné, J., Sur les groupes classiques, Actualités Sci. Ind. No. 1040, Hermann, Paris 1948.
Dyck, W., “Gruppentheoretische Studien II. Über die Zusammensetzung einer Gruppe discreter Operationen, über ihre Primitivität und Transitivität,” Math. Ann. 22 (1883), 70–108.
Fricke, R., & F. Klein, Vorlesungen über die Theorie der automorphen Funktionen, volume I, Johnson Reprint, New York, 1965.
Frobenius, G., Gesammelte Abhandlungen, 3 volumes, Springer, Berlin, New York, 1968.
Gallian, J., “The Search for Finite Simple Groups,” Math. Magazine, 49 (1976), 164–179.
Galois, E., “Œuvres,” Journ. Math. Pure. Appl. 11 (1846), 381–444.
Galois, E., Œuvres Mathématiques, Gauthier-Villars, Paris, 1897.
Galois, E., Ecrits et Mémoires Mathématiques (ed. by R. Bourgne & J.P. Azra), Gauthier-Villars, Paris, 1962.
Gierster, J., “Die Untergruppen der Galois'schen Gruppe der Modulargleichungen für den Fall eines primzahligen Transformationsgrades,” Math. Ann. 18 (1881), 319–365.
Gordan, P., “Über Gleichungen siebenten Grades mit einer Gruppe von 168 Substitutionen,” Math. Ann. 20 (1882), 515–520.
Gordan, P., “Über Gleichungen siebenten Grades mit einer Gruppe von 168 Substitutionen II,” Math. Ann. 25 (1885), 459–521.
Hermite, C., “Considérations sur la résolution algébrique de l'équation du 5e degré,” Nouvelles Annales de Mathematiques 1 (1842), 329–336.
Hölder, O., “Zurückführung einer beliebigen algebraischen Gleichung auf eine Kette von Gleichungen,” Math. Ann. 34 (1889), 26–56.
Hölder, O., “Die einfachen Gruppen im ersten und zweiten Hundert der Ordnungszahlen,” Math. Ann. 40 (1892), 55–88.
Jordan, C., Œuvres, 4 volumes, Gauthier-Villars, Paris, 1961–1964.
Jordan, C., Traité des Substitutions et des Equations Algébriques, Gauthier-Villars, Paris, 1870.
Kiernan, B. M., “The development of Galois theory from Lagrange to Artin,” Arch. History Exact Sci. 8 (1971), 40–154.
Kirkman, T. P., “The complete theory of groups,” Proc. Lit. Phil. Soc. Manchester 3 (1864), 133–152.
Kirkman, T. P., “Theory of groups, corrigenda and addenda,” Proc. Lit. Phil. Soc. Manchester 4 (1865), 171–172.
Klein, F., Lectures on the Icosahedron and the Solution of Equations of the Fifth Degree, trans. by G. G. Morrice, Kegan Paul, Trench, Teubner & Co., London, 1888.
Klein, F., Gesammelte Mathematische Abhandlungen, 3 volumes, Reprint, Springer-Verlag, Berlin, New York, 1973.
Kline, M., Mathematical Thought from Ancient to Modern Times, Oxford University Press, New York, 1972.
Mathieu, E., “Mémoire sur le nombre de valeurs que peut acquerir une fonction,” C.R. Acad. Sci. Paris 48 (1859), 840–841.
Mathieu, E., “Mémoire sur le nombre de valeurs que peut acquérir une fonction quand on y permute ses variables de toutes les manières possibles,” Jour. Math. Pures Appl. (2) 5 (1860), 9–42.
Mathieu, E., “Mémoire sur l'étude des fonctions de plusieurs quantités, sur la manière de les former et sur les substitutions qui les laissent invariables,” Jour. Math. Pures Appl. (2) 6 (1861), 241–323.
Mathieu, E., “Sur la fonction cinq fois transitive des 24 quantités,” Journ. Math. Pures Appl. (2) 18 (1873), 25–46.
Miller, G. A., Collected Works, 5 volumes, Univ. of Illinois Press, Urbana, 1935–1959.
Moore, E. H., “A doubly infinite system of simple groups,” Chicago Math. Congress Papers (1893), 208–242.
Netto, E., Theory of Substitutions and its Applications to Algebra, trans. by F. N. Cole, George Wahr, Ann Arbor, 1892.
Rotman, J., The Theory of Groups: An Introduction, Allyn & Bacon, Boston, 1965.
Ruffini, P., “Lettera di Pietro Abbati Modenese al socio,” Memorie della Società Italiana delle Scienze 10 (1803), 385–409.
Schläfli, L., “An attempt to determine the 27 lines upon a surface of the third order,” Quart. J. Pure Appl. Math. 2 (1858), 110–120.
Schottenfels, I., “Two non-isomorphic simple groups of the same order 20,160,” Annals of Math. (2) 1 (1900), 147–152.
Serret, J., “Sur les fonctions de quatre, cinq et six lettres,” Jour. Math. Pures Appl. (1) 15 (1850), 45–70.
Serret, J., Cours d'algèbre supérieure, third ed., 2 volumes, Gauthier-Villars, Paris, 1866.
Siceloff, L. P., “Simple groups from order 2001 to order 3640,” Bull. Amer. Math. Soc. (2) 18 (1911), 161–162.
Smith, D. E., A Source Book in Mathematics, McGraw-Hill, New York, 1929.
Steiner, J., “Über die Flächen dritten Grades,” J. Reine Angew. Math. 53 (1856), 133–141.
Sylow, L., “Théorèmes sur les groupes des substitutions,” Math. Ann. 5 (1872), 584–594.
Weber, H., Lehrbuch der Algebra, 2 volumes, F. Vieweg & Sohn, Braunschweig, 1895–1896.
Weyl, H., The Classical Groups, second ed., University Press, Princeton, 1946.
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Communicated by M. Kline
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Silvestri, R. Simple groups of finite order in the nineteenth century. Arch. Rational Mech. 20, 313–356 (1979). https://doi.org/10.1007/BF00327738
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DOI: https://doi.org/10.1007/BF00327738