Groups where all the irreducible characters are super-monomial

Details Groups where all the irreducible characters are super-monomial Groups where all the irreducible characters are super-monomial

2008-12-11

arxiv.org/abs/0812.2220v1

Mathematics

Group Theory

Scientific paper

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 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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