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On ๐”“-Adic Integral Representations of Finite Groups

Published online by Cambridge University Press:ย  20 November 2018

Jean-Marie Maranda
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It has been shown by Diederichsen [2] that for integral representations of a finite group, the irreducible constituents in any complete reduction are not necessarily unique up to order and unimodular equivalence. In this same article, it is shown that for certain finite groups, such as the cyclic group of order 4, there are infinitely many classes of indecomposable representations under unimodular equivalence.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 5 , 1953 , pp. 344 - 355
Copyright
Copyright ยฉ Canadian Mathematical Society 1953

References

1. Brauer, R. and Nesbitt, C., On the modular representations of groups of finite order, University of Toronto Studies, Math. Series, no. 4 (1937).Google Scholar
2. Diederichsen, F. E., รœber die Ausreduktion ganzzahliger Gruppendarstellungen bei ariihtnetischer Jquivalenz, Abh. Math. Sem. Hansischen Univ., 14 (1938), 357โ€“412.Google Scholar
3. van der Waerden, B. L., Moderne Algebra, 2nd ed. (New York, 1943).Google Scholar
4. Zassenhaus, H., Neuer Beweis der Endlichkeit der Klassenzahl bei unimodularer Aquivalenz endlicher ganzzahliger Substitutionsgruppen, Abh. Math. Sem. Hansischen Univ., 12 (1938), 276โ€“288.Google Scholar