Finite Group Elements where No Irreducible Character Vanishes

Finite Group Elements where No Irreducible Character Vanishes

In this paper, we consider elements x of a finite group G with the property that χ(x)≠0 for all irreducible characters χ of G. If G is solvable and x has odd order, we show that x must lie in the Fitting subgroup F(G).

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Veröffentlicht in:Journal of algebra 1999-12, Vol.222 (2), p.413-423
Hauptverfasser: Isaacs, I.M, Navarro, Gabriel, Wolf, Thomas R
Format: Artikel
Sprache:eng
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Zusammenfassung:In this paper, we consider elements x of a finite group G with the property that χ(x)≠0 for all irreducible characters χ of G. If G is solvable and x has odd order, we show that x must lie in the Fitting subgroup F(G).
ISSN:0021-8693
1090-266X
DOI:10.1006/jabr.1999.8007