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On the arithmetical character of the coefficients of the substitutions of finite linear substitutions groups. (Ueber den arithmetischen Charakter der Coefficienten der Substitutionen endlicher linearer Substitutionsgruppen.) (German) JFM 29.0114.03

MSC:
20B99Permutation groups
References:
[1]Wie zuerst von Herrn Camille Jordan angegeben (Mémoire sur les équations différentielles linéaires à intégrale algebrique, Journ. für Math. Bd. 84, pag. 112).
[2]Vgl. H. Maschke, die Reduction linearer Substitutionen von endlicher Periode auf ihre kanonische Form. Math. Ann. Bd. L, pag. 220.
[3]Die Herleitungsmethode dieser Gleichungen, so wie auch später der Gleichungen (6) und (8) ist analog der Methode, vermittelst welcher Herr Valentiner (De endelige Transformations-Gruppers Theori, Kopenhangen, 1889) und Herr Fuchs (Ueber eine Classe linearer homogener Differentialgleichungen, Berliner Sitzungsberichte, XXXIV, 1896) ähnliche Gleichungen zur Erreichung anderer Resultate bilden.
[4]Dieser Satz ist bereits von Valentiner l. c. Herr Valentiner (De endelige Transformations-Gruppers Theori, Kopenhagen, 1889) pag. 93-95 in wesentlich derselben Weise bewiesen worden.
[5]Vgl. E. H. Moore, A Universal Invariant for Finite Groups of Linear Substitutions. Math. Ann. Bd. 50, pag. 213.
[6]Zu ähnlichen Formeln gelangt auch Valentiner und Fuchs. l. c. Herr Fuchs (Ueber eine Classe linearer homogener Differentialgleichungen, Berliner Sitzungsberichte, XXXIV, 1896)