Groups where all the irreducible characters are super-monomial
Group Theory
2008-12-12 v1
Abstract
Isaacs has defined a character to be super monomial if every primitive character inducing it is linear. Isaacs has conjectured that if is an -group with odd order, then every irreducible character is super monomial. We prove that the conjecture is true if is an -group of odd order where every irreducible character is a -lift for some prime . We say that a group where irreducible character is super monomial is a super -group. We use our results to find an example of a super -group that has a subgroup that is not a super -group.
Cite
@article{arxiv.0812.2220,
title = {Groups where all the irreducible characters are super-monomial},
author = {Mark L. Lewis},
journal= {arXiv preprint arXiv:0812.2220},
year = {2008}
}