Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-25T15:00:35.918Z Has data issue: false hasContentIssue false
  • English
  • Français

On The Equivalence Of Representations Of Finite Groups By Groups Of Automorphisms Of Modules Over Dedekind Rings

Published online by Cambridge University Press:  20 November 2018

J.-M. Maranda
J.-M. Maranda*
Affiliation:
Université de Montréal
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let t be a Dedekind ring whose quotient field we denote by K. If is a prime ideal of t, let o denote the ring of all -regular elements of K. If is a torsion free i-module, let K denote the smallest K-module into which can be embedded and let o denote the o-submodule of K generated by .

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 7 , 1955 , pp. 516 - 526
Copyright
Copyright © Canadian Mathematical Society 1955

References

1. Kaplansky, I., Modules over Dedekind rings and valuation rings, Trans. Amer. Math. Soc., 72 (1952), 327–340.Google Scholar
2. Maranda, J.-M., On -adic integral representations of finite groups, Can. J. Math., 5 (1953), 344–355.Google Scholar
3. Schur, I., Arithmetische Untersuchungen iiber endliche Gruppen linearer Substitutionen, Berl. Ber. (1906), 164–184.Google Scholar
4. Steinitz, E., Rechteckige Systeme und Moduln in algebraischen Zahlkorpern, Math. Ann. I, 71 (1911), 328–354, II, 72 (1912), 297–345.Google Scholar
5. Zassenhaus, H., Neuer Beweis der Endlichkeit der Klassenzahl bei unimodularer Äquivalenz endhcher ganzzahliger Substitutions gruppen, Abh. Math. Sem. Hansischen Univ. 12 (1938), 276–288.Google Scholar
6. Zassenhaus, H., The theory of groups (New York, 1949).Google Scholar