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Original Articles

What's Abelian about abelian groups?

Pages 37-51 | Published online: 07 Jan 2013

Bibliography

  • Abel , N H . 1824 . “ Mémoire sur les équations algébriques, on l'on démontre l'impossibilité de la résolution de l'équation générale du cinquième degré ” . In Oeuvres Complètes de Niels Henrik Abel , Edited by: Sylow , L and Lie , S . Vol. 1 , 28 – 33 . Christiania : Grøndahl .
  • Abel , N H . 1826 . Beweis der Unmöglichkeit, algebraische Gleichungen von höheren Graden, als dem vierten, allgemein aufzulösen . Journal für die reine und angewandte Mathematik , 1 : 65 – 84 .
  • Abel , N H . 1827 . Recherches sur les fonctions elliptiques . Journal für die reine und angewandte Mathematik , 2 : 101 – 181 .
  • Abel , N H . [1828] 1839 . “ Sur la résolution algébrique des équations ” . In Oeuvres Complètes de Niels Henrik Abel , Edited by: Sylow , L and Lie , S . Vol. 2 , 217 – 243 . Christiania : Grøndahl .
  • Abel , N H . 1828 . Recherches sur les fonctions elliptiques . Journal für die reine und angewandte Mathematik , 3 : 160 – 190 .
  • Abel , N H . 1829 . Mémoire sur une classe particulière d'équations résolubles algébriquement . Journal für die reine und angewandte Mathematik , 4 : 131 – 156 .
  • Abel , N H . in B M Holmboe (ed), Oeuvres Complètes de N. H. Abel, mathématicien, avec desnotes et développements, Christiania: Chr. Gröndahl, 1839
  • Abel , N H . in L Sylow and S. Lie (eds), Oeuvres Complètes de Niels Henrik Abel, Christiania: Grøndahl, 1881
  • Abel , N H . 1902 . “ Breve fra og til Abel ” . In Festskrift ved Hundredeaarsjubilæet for Niels Henrik Abels Fødsel , Edited by: Holst , E , Størmer , C and Sylow , L . Kristiania : Jacob Dybwad .
  • Ayoub , R . 1980 . Paolo Ruffni's Contributions to the Quintic . Archive for History of Exact Sciences , 23 : 253 – 277 .
  • Ayoub , R . 1984 . The Lemniscate and Fagnano's Contributions to Elliptic Integrals . Archive for History of Exact Sciences , 29 : 131 – 149 .
  • Cauchy , A-L . 1815 . “ Mémoire sur le nombre des valeurs qu'une fonction peut acquérir, lorsqu'on y permute de toutes les manières possibles les quantités qu'elle renferme ” . In Euvres Complètes d'Augustin Cauchy , Vol. II.1 , 64 – 90 . Paris : Gauthier-Villars .
  • Epple , M . 2011 . Between timelessness and historiality: on the dynamics of the epistemic objects of mathematics . Isis , 102 : 481 – 493 .
  • Gauss , C F . 1801 . “ Disquisitiones arithmeticae ” . In Carl Friedrich Gauss Werke , Vol. 1 , 1973 – 1981 . Reprinted Georg Olms Verlag . Göttingen: Königliche Gesellschaft der Wissenschaften, 3–474
  • Gauss , C F . 1981 . “ Mathematisches Tagebuch 1796–1814 ” . In Ostwalds Klassiker der exakten Wissenschaften 256 , Leipzig : Akademische Verlagsgesellschaft, Geest & Portig K-G .
  • Gauss , C F . 1986 . Disquisitiones Arithmeticae English edition , Edited by: Clarke , A A and Waterhouse , W C . Springer-Verlag .
  • Gray , J J . 1990 . “ Herausbildung von strukturellen Grundkonzepten der Algebra im 19. Jahrhundert ” . In Geschichte der Algebra: eine Einführung , Edited by: Scholz , E . 293 – 323 . Lehrbücher und Monographien zur Didaktik der Mathematik 16. Mannheim, Wien, and Zürich: Bibliographisches Institut, Wissenschaftsverlag . Chap. 11
  • Gårding , L and Skau , C . 1994 . Niels Henrik Abel and solvable equations . Archive for History of Exact Sciences , 48 : 81 – 103 .
  • Holst , E , Størmer , C and Sylow , L (eds) . 1902 . “ Breve om Abel ” . In Festskrift ved Hundredeaarsjubilæet for Niels Henrik Abels Fødsel , Kristiania : Jacob Dybwad .
  • Houzel , C . 2004 . “ The work of Niels Henrik Abel ” . In The legacy of Niels Henrik Abel. The Abel Bicentennial, Oslo, 2002 , Edited by: Laudal , O A and Piene , R . 21 – 177 . Springer .
  • Kiernan , B M . 1971 . The Development of Galois Theory from Lagrange to Artin . Archive for History of Exact Sciences , 8 : 40 – 154 .
  • Lagrange , J-L . 1770–71 . “ Réflexions sur la résolution algébrique des équations ” . In Euvres de Lagrange Edited by: Serret , J-A . Vol. 3 , 203 – 421 . Paris
  • Lemmermeyer , F and Roquette , P (eds) . 2006 . Helmut Hasse und Emmy Noether. Die Korrespondenz 1925–1935 , Universitätsverlag Göttingen .
  • Lützen , J . 2009 . Why was Wantzel overlooked for a century? The changing importance of an impossibility result . Historia Mathematica , 36 : 374 – 394 .
  • Neumann , O . 2007 . “ Disquisitiones arithmeticae and the theory of equations ” . In The shaping of arithmetic after C. F. Gauss's Disquisitiones arithmeticae , Edited by: Goldstein , C , Schappacher , N and Schwermer , J . 107 – 127 . Springer . Chap. II.1
  • Ore , Ø . 1957 . Niels Henrik Abel: mathematician extraordinary , University of Minnesota Press .
  • Rosen , M . 1981 . Abel's theorem on the lemniscate . The American Mathematical Monthly , 88 : 387 – 395 .
  • Scholz , E . 1990 . “ Die Entstehung der Galoistheorie ” . In Geschichte der Algebra: eine Einführung , Edited by: Scholz , E . 365 – 398 . Lehrbücher und Monographien zur Didaktik der Mathematik 16, Mannheim, Wien, and Zürich: Bibliographisches Institut, Wissenschaftsverlag .
  • Sørensen , H K . 2005 . Exceptions and counterexamples: understanding Abel's comment on Cauchy's Theorem . Historia Mathematica , 32 : 453 – 480 .
  • Sørensen , H K . 2009 . “ Representations as means and ends: representability and habituation in mathematical analysis during the first part of the nineteenth century ” . In New perspectives on mathematical practices: essays in philosophy and history of mathematics , Edited by: Van Kerkhove , B . 114 – 137 . World Scientific .
  • Sørensen , H K . 2010a . The mathematics of Niels Henrik Abel: continuation and new approaches in mathematics during the 1820s , RePoSS: Research Publications on Science Studies 11, University of Aarhus . Oct http://www.css.au.dk/reposs
  • Sørensen , H K . 2010b . Throwing some light on the vast darkness that is analysis: Niels Henrik Abel's critical revision and the concept of absolute convergence . Centaurus , 52 : 38 – 72 .
  • Stubhaug , A . 1996 . Et foranskutt lyn — Niels Henrik Abel og hans tid , Aschehoug .
  • Stubhaug , A . 2000 . Niels Henrik Abel and his times: called too soon by flames afar , Springer .
  • Toti Rigatelli , L . 1994 . “ The theory of equations from Cardano to Galois 1540–1830 ” . In Companion encyclopedia of the history and philosophy of the mathematical sciences , Edited by: Grattan-Guinness , I . 713 – 721 . London : Routledge .
  • Waerden , B L van der . 1930/1931 . “ Moderne Algebra ” . In Die Grundlehren der mathematischen Wissenschaften 33 – 34 . Berlin
  • Weber , H . 1895/1896 . Lehrbuch der Algebra Braunschweig
  • Wussing , H . ‘Implizite gruppentheoretische Denkformen in den “Disquisitiones arithmeticae” von Carl Friedrich Gauß’, in M Behara, R Fritsch, and R G Lintz (eds), Symposia Gaussiana. Proceedings of the 2nd Gauss Symposium. Conference A: Mathematics and Theoretical Physics. Munich, Germany, August 2–7, 1993, Walter de Gruyter, 1995, 179–185
  • Wussing , H . 2007 . The genesis of the abstract group concept: a contribution to the history of the origin of abstract group theory , Dover Publications .

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