Groups where all the irreducible characters are super-monomial
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- by Mark L. Lewis PDF
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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.References
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Additional Information
- Mark L. Lewis
- Affiliation: Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242
- MR Author ID: 363107
- Email: lewis@math.kent.edu
- Received by editor(s): December 15, 2008
- Published electronically: August 13, 2009
- Communicated by: Jonathan I. Hall
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 9-16
- MSC (2000): Primary 20C15
- DOI: https://doi.org/10.1090/S0002-9939-09-10059-X
- MathSciNet review: 2550165