Groups where all the irreducible characters are super-monomial

Author:
Mark L. Lewis

Journal:
Proc. Amer. Math. Soc. **138** (2010), 9-16

MSC (2000):
Primary 20C15

DOI:
https://doi.org/10.1090/S0002-9939-09-10059-X

Published electronically:
August 13, 2009

MathSciNet review:
2550165

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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 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 every 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.

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Additional Information

**Mark L. Lewis**

Affiliation:
Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242

Email:
lewis@math.kent.edu

DOI:
https://doi.org/10.1090/S0002-9939-09-10059-X

Keywords:
$\pi $-partial characters,
lifts,
$M$-groups,
super monomial characters

Received by editor(s):
December 15, 2008

Published electronically:
August 13, 2009

Communicated by:
Jonathan I. Hall

Article copyright:
© Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.