English

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 GG is an MM-group with odd order, then every irreducible character is super monomial. We prove that the conjecture is true if GG is an MM-group of odd order where every irreducible character is a {p}\{p \}-lift for some prime pp. We say that a group where irreducible character is super monomial is a super MM-group. We use our results to find an example of a super MM-group that has a subgroup that is not a super MM-group.

Keywords

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}
}
R2 v1 2026-06-21T11:51:00.600Z