Groups where all the irreducible characters are supermonomial
Author:
Mark L. Lewis
Journal:
Proc. Amer. Math. Soc. 138 (2010), 916
MSC (2000):
Primary 20C15
Published electronically:
August 13, 2009
MathSciNet review:
2550165
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Abstract: Isaacs has defined a character to be supermonomial if every primitive character inducing it is linear. Isaacs has conjectured that if is an group with odd order, then every irreducible character is supermonomial. 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 supermonomial 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:
http://dx.doi.org/10.1090/S000299390910059X
PII:
S 00029939(09)10059X
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.
