@article{61c12a986ccd42eeb6f48bdf59c7637c,

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: dolfi@math.unifi.it (S. Dolfi), gabriel@uv.es (G. Navarro), emanuele.pacifici@unimi.it (E. Pacifici), lucia.sanus@uv.es (L. Sanus), tiep@math.arizona.edu (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",

}