Primes dividing the degrees of the real characters

Silvio Dolfi, Gabriel Navarro, Pham Huu Tiep

Research output: Contribution to journalArticlepeer-review

40 Scopus citations

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 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.

Original languageEnglish (US)
Pages (from-to)755-774
Number of pages20
JournalMathematische Zeitschrift
Volume259
Issue number4
DOIs
StatePublished - Aug 1 2008

ASJC Scopus subject areas

  • Mathematics(all)

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