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math.HO2026
The Significance of Proposition II in Galois' Mémoire, The Origin of Galois Automorphisms
Math Dicker
In Proposition II of his manuscript, Galois writes the well-known remark: Il y a quelque chose à compléter dans cette démonstration. Je n'ai pas le temps. Although Galois did not c…
math.HO2026
Adolf Hurwitz and the Fundamental Theorem of Galois Theorie: The Königsberg Lectures of 1890-1891
Math Dicker
In the winter semester of 1890--1891 Adolf Hurwitz delivered a lecture course at the Albertina University in Königsberg entitled -Theorie der algebraischen Gleichungen-. These lect…
math.HO2019
The main theorem of the Galois theory proven with ideas from the first Mémoire of Galois
Math Dicker
A proof of the main theorem of the Galois theory is presented using the main theorem of symmetric polynomials. The idea originated from studying the "Mémoire sur les conditions de…
math.HO2012
A proof of the Quadratic Reciprocity Law
Math Dicker
A proof of the Quadratic Reciprocity Law is presented using a Lemma of Gauss, the theory of finite fields and the Frobenius automorfism.