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Classification of solvable groups possessing a unique nonlinear non-faithful irreducible character

Amin Saeidi — 2014

Open Mathematics

In this note, we study finite groups possessing exactly one nonlinear non-faithful irreducible character. Our main result is to classify solvable groups that satisfy this property. Also, we give examples to show that these groups need not to be solvable in general.

Finite groups with a unique nonlinear nonfaithful irreducible character

Ali Iranmanesh; Amin Saeidi — 2011

Archivum Mathematicum

In this paper, we consider finite groups with precisely one nonlinear nonfaithful irreducible character. We show that the groups of order 16 with nilpotency class 3 are the only $p$ -groups with this property. Moreover we completely characterize the nilpotent groups with this property. Also we show that if $G$ is a group with a nontrivial center which possesses precisely one nonlinear nonfaithful irreducible character then $G$ is solvable.

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