@article{cfd78a5ed2ad4d81939bdfded8d300af,
title = "Non-vanishing elements of finite groups",
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.",
keywords = "Characters, Finite groups, Zeros of characters",
author = "Silvio Dolfi and Gabriel Navarro and Emanuele Pacifici and Lucia Sanus and Tiep, {Pham Huu}",
note = "Funding Information: ✩ Part of the paper was written while the fifth author participated in the Algebraic Lie Theory Program of the Isaac Newton Institute for Mathematical Sciences (Cambridge, 2009). It is a pleasure to thank the organizers and the Newton Institute for their generous hospitality and support. ✩✩ The research of the first and third authors is partially supported by the MIUR project “Teoria dei gruppi e applicazioni”. The research of the second and fourth authors is partially supported by the Spanish Ministerio de Educaci{\'o}n y Ciencia proyecto MTM2007-61161. The fifth author gratefully acknowledges the support of the NSF (grant DMS-0600967). * Corresponding author. E-mail addresses:
[email protected] (S. Dolfi),
[email protected] (G. Navarro),
[email protected] (E. Pacifici),
[email protected] (L. Sanus),
[email protected] (P.H. Tiep).",
year = "2010",
month = jan,
day = "15",
doi = "10.1016/j.jalgebra.2009.08.014",
language = "English (US)",
volume = "323",
pages = "540--545",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "Academic Press Inc.",
number = "2",
}