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Archiv der Mathematik

, Volume 71, Issue 5, pp 358–367 | Cite as

Casimir-Operator und ein Satz von Reynolds über Charaktergrade

  • Manfred Leitz
Article

Abstract.

The following result concerning character degrees is familiar. Let H be a normal subgroup of the finite group G with the identity e. Furthermore let \(\theta \) be an irreducible complex character of H, and \(\chi \) be an irreducible complex character of G with \(\big (\theta ^G,\chi \big )_G \ne 0\). Then the co-degree \(|H|/\theta (e)\) divides the co-degree \(|G|/\chi (e)\). The usual proof rests on Schur's theory of projective representations and on Clifford's theory. The purpose of this paper is to give a more elementary proof based on the so-called Casimir operator.

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Copyright information

© Birkhäuser Verlag, Basel 1998

Authors and Affiliations

  • Manfred Leitz
    • 1
  1. 1.Fachbereich Informatik und Mathematik, Fachhochschule Regensburg, Postfach 12 03 27, D-93025 Regensburg, GermanyDeutschland

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