Groups where all the irreducible characters are super-monomial

Lewis, Mark

doi:10.1090/S0002-9939-09-10059-X

Groups where all the irreducible characters are super-monomial
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by Mark L. Lewis PDF

Proc. Amer. Math. Soc. 138 (2010), 9-16 Request permission

Abstract:

Isaacs has defined a character to be super-monomial if every primitive character inducing it is linear. Isaacs has conjectured that if $G$ is an $M$-group with odd order, then every irreducible character is super-monomial. We prove that the conjecture is true if $G$ is an $M$-group of odd order where every irreducible character is a $\{p\}$-lift for some prime $p$. We say that a group where every irreducible character is super-monomial is a super $M$-group. We use our results to find an example of a super $M$-group that has a subgroup that is not a super $M$-group.

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