Mathematische Zeitschrift

, 259:755 | Cite as

Primes dividing the degrees of the real characters

Article

Abstract

Let G be a finite group and let Irr(G) denote the set of all complex irreducible characters of G. The Ito–Michler Theorem asserts that if a prime p does not divide the degree of any χ \(\in\) Irr(G) then a Sylow p-subgroup P of G is normal in G. We prove a real-valued version of this theorem, where instead of Irr(G) we only consider the subset Irrrv(G) consisting of all real-valued irreducible characters of G. We also prove that the character degree graph associated to Irrrv(G) has at most 3 connected components. Similar results for the set of real conjugacy classes of G have also been obtained.

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di FirenzeFlorenceItaly
  2. 2.Departament d’ÀlgebraUniversitat de ValènciaBurjassotSpain
  3. 3.Department of MathematicsUniversity of FloridaGainesvilleUSA

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