Cauchy's theorem on the order of finite groups is a fixture of elementary course work in abstract algebra today. Its proof is a straightforward exercise in the application of general mathematical tools. The initial proof by Cauchy, however, was unprecedented in its complex computations involving permutational group theory and contained an egregious error. A direct inspiration to Sylow's theorem, Cauchy's theorem was reworked by R. Dedekind, G.F. Frobenius, C. Jordan, and J.H. McKay in ever more natural, concise terms. Its most succinct form employs just the structure lacking in Cauchy's original proof, the wreath product.
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Book
Hollings, Christopher David;
(2014)
Mathematics across the Iron Curtain: A History of the Algebraic Theory of Semigroups
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Ehrhardt, Caroline;
(2011)
Évariste Galois: La fabrication d'une icône mathématique
(/isis/citation/CBB001221115/)
Article
Sørensen, Henrik Kragh;
(2013)
What's Abelian about Abelian Groups?
(/isis/citation/CBB001212298/)
Article
Ehrhardt, Caroline;
(2011)
Évariste Galois and the Social Time of Mathematics
(/isis/citation/CBB001221117/)
Book
Cauchy, Augustin-Louis;
Pérez Fernández, F. Javier;
Díaz Moreno, José M.;
(1998)
Cours d'analyse de l'Ecole Royale Polytechnique
(/isis/citation/CBB000530050/)
Article
Boucard, Jenny;
(2013)
Cyclotomie et formes quadratiques dans l'œuvre arithmétique d'Augustin-Louis Cauchy (1829--1840)
(/isis/citation/CBB001211763/)
Article
Boucard, Jenny;
(2013)
Cyclotomie et formes quadratiques dans l'œuvre arithmétique d'Augustin-Louis Cauchy (1829--1840)
(/isis/citation/CBB001253129/)
Book
Ronan, Mark;
(2006)
Symmetry and the Monster: One of the Greatest Quests of Mathematics
(/isis/citation/CBB000640789/)
Article
Christopher D. Hollings;
(2017)
‘Nobody Could Possibly Misunderstand What a Group Is’: A Study in Early Twentieth-Century Group Axiomatics
(/isis/citation/CBB787330938/)
Article
Hollings, Christopher;
(2009)
The Early Development of the Algebraic Theory of Semigroups
(/isis/citation/CBB000932084/)
Article
Frisch, Uriel;
Villone, Barbara;
(2014)
Cauchy's Almost Forgotten Lagrangian Formulation of the Euler Equation for 3D Incompressible Flow
(/isis/citation/CBB001451853/)
Book
Burnside, William;
Neumann, Peter M.;
Mann, A. J. S.;
Tompson, Julia C.;
(2004)
The Collected Papers of William Burnside
(/isis/citation/CBB000650385/)
Article
Hawkins, Thomas;
(1975)
Cauchy and the spectral theory of matrices
(/isis/citation/CBB000021000/)
Article
Adelmann, Clemens;
Gerbracht, Eberhard H.-A.;
(2009)
Letters From William Burnside to Robert Fricke: Automorphic Functions, and the Emergence of the Burnside Problem
(/isis/citation/CBB000932072/)
Book
Schneider, Martina R;
(2011)
Zwischen zwei Disziplinen: B. L. van der Waerden und die Entwicklung der Quantenmechanik
(/isis/citation/CBB001420968/)
Article
James V. Rauff;
(2016)
The Algebra of Marriage: An Episode in Applied Group Theory
(/isis/citation/CBB687142450/)
Article
Neumann, Peter M.;
(2006)
The Concept of Primitivity in Group Theory and the Second Memoir of Galois
(/isis/citation/CBB000670790/)
Chapter
Giulia Giannini;
(2009)
Poincaré, la nozione di gruppo e il Programma di Erlangen di F. Klein
(/isis/citation/CBB227666735/)
Article
Wußing, Hans;
(2008)
Arthur Cayley und der abstrakte Gruppenbegriff
(/isis/citation/CBB001021147/)
Article
Dahan, Amy;
(1980)
Les travaux de Cauchy sur les substitutions: Étude de son approche du concept de groupe
(/isis/citation/CBB000009970/)
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