Feit numbers and \(p'\)-degree characters

Suppose that \(\chi\) is an irreducible complex character of \(G\) and let \(f_\chi\) be the smallest integer \(n\) such that the cyclotomic field \(\mathbb Q_n\) contains the values of \(\chi\). Let \(p\) be a prime, and assume that \(\chi \in \textrm{Irr}(G)\) has degree not divisible by \(p\). If...

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Bibliographic Details
Published inarXiv.org
Main Author Carolina Vallejo Rodríguez
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 13.01.2016
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Summary:Suppose that \(\chi\) is an irreducible complex character of \(G\) and let \(f_\chi\) be the smallest integer \(n\) such that the cyclotomic field \(\mathbb Q_n\) contains the values of \(\chi\). Let \(p\) be a prime, and assume that \(\chi \in \textrm{Irr}(G)\) has degree not divisible by \(p\). If \(G\) is solvable and \(\chi(1)\) is odd, then there exists \(g \in {\bf N}_G(P) /P'\) with \(o(g)=f_\chi\). In particular \(f_\chi\) divides \(|{\bf N}_G(P) /P'|\).
ISSN:2331-8422