Let G be a finite group, and let Irr(G) denote the set of irreducible complex characters of G. An element x of G is non-vanishing if, for every χ in Irr(G), we have χ(x)≠0. We prove that, if x is a non-vanishing element of G and the order of x is coprime to 6, then x lies in the Fitting subgroup of G.
Non-vanishing elements of finite groups / S. Dolfi, G. Navarro, E. Pacifici, L. Sanus, P.H. Tiep. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - 323:2(2010 Jan), pp. 540-545.
Non-vanishing elements of finite groups
E. Pacifici;
2010
Abstract
Let G be a finite group, and let Irr(G) denote the set of irreducible complex characters of G. An element x of G is non-vanishing if, for every χ in Irr(G), we have χ(x)≠0. We prove that, if x is a non-vanishing element of G and the order of x is coprime to 6, then x lies in the Fitting subgroup of G.
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