Finite groups with a unique nonlinear nonfaithful irreducible character. (Q2897381)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Finite groups with a unique nonlinear nonfaithful irreducible character. |
scientific article; zbMATH DE number 6054249
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Finite groups with a unique nonlinear nonfaithful irreducible character. |
scientific article; zbMATH DE number 6054249 |
Statements
10 July 2012
0 references
nonlinear irreducible characters
0 references
finite groups
0 references
minimal normal subgroups
0 references
faithful characters
0 references
Frobenius groups
0 references
Finite groups with a unique nonlinear nonfaithful irreducible character. (English)
0 references
All finite groups, which have exactly one nonlinear irreducible character, were classified by \textit{Y. Berkovich, D. Chillag} and \textit{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.
0 references
