Iranmanesh, Ali; Saeidi, Amin Finite groups with a unique nonlinear nonfaithful irreducible character. (English) Zbl 1249.20009 Arch. Math., Brno 47, No. 2, 91-98 (2011). All finite groups, which have exactly one nonlinear irreducible character, were classified by Y. Berkovich, D. Chillag and M. Herzog [Proc. Am. Math. Soc. 115, No. 4, 955-959 (1992; Zbl 0822.20004)]. Based on this result, finite groups, which have exactly one nonlinear nonfaithful irreducible character, are studied in this paper. In particular, it is shown that the only \(p\)-groups with this property are groups of order \(16\) and of nilpotency class \(3\), and a complete classification of nilpotent groups with this property is given. Reviewer: Michal Kunc (Brno) Cited in 2 ReviewsCited in 7 Documents MSC: 20C15 Ordinary representations and characters 20D15 Finite nilpotent groups, \(p\)-groups Keywords:nonlinear irreducible characters; finite groups; minimal normal subgroups; faithful characters; Frobenius groups Citations:Zbl 0822.20004 PDFBibTeX XMLCite \textit{A. Iranmanesh} and \textit{A. Saeidi}, Arch. Math., Brno 47, No. 2, 91--98 (2011; Zbl 1249.20009) Full Text: EuDML EMIS