Finite Groups with Only One NonLinear Irreducible Representation

Abstract

Let 𝕂 be an algebraically closed field. We classify the finite groups having exactly one irreducible 𝕂-representation of degree bigger than one. The case where the characteristic of 𝕂 is zero, was done by G. Seitz in 1968.

Key Words:

• Finite groups
• Representations

2000 Mathematics Subject Classification:

• 20C15
• 20D20

ACKNOWLEDGMENTS

The first author is partially supported by MURST project “Teoria dei Gruppi e Applicazioni.” The second author is partially supported by the Ministerio de Educación y Ciencia proyecto MTM2010-15296, Programa de Movilidad, and Prometeo/Generalitat Valenciana.

Notes

Communicated by A. Turull.