Primes dividing the degrees of the real characters

Silvio Dolfi, Gabriel Navarro, Pham Huu Tiep

Research output: Contribution to journalArticle

33 Citations (Scopus)

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 2008
Externally publishedYes

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Irreducible Character
Character Degrees
Conjugacy class
Theorem
Connected Components
Divides
Finite Group
Subgroup
Denote
Subset
Graph in graph theory
Character

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Primes dividing the degrees of the real characters. / Dolfi, Silvio; Navarro, Gabriel; Tiep, Pham Huu.

In: Mathematische Zeitschrift, Vol. 259, No. 4, 08.2008, p. 755-774.

Research output: Contribution to journalArticle

Dolfi, Silvio ; Navarro, Gabriel ; Tiep, Pham Huu. / Primes dividing the degrees of the real characters. In: Mathematische Zeitschrift. 2008 ; Vol. 259, No. 4. pp. 755-774.
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