On super-monomial characters and groups having two irreducible monomial character degrees

2019/04/28 by Færgeman, Joakim
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1904.12377

Abstract

A character of a group is said to be super-monomial if every primitive character inducing it is linear. It is conjectured by Isaacs that every irreducible character of an odd M-group is super-monomial. We show that all non linear irreducible characters of lowest degree of an odd M-group is super-monomial and provide cases in which one can guarantee that certain irreducible characters of normal subgroups are super-monomial. Finally, we study groups having two irreducible monomial character degrees.

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