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Proceedings of the American Mathematical Society

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Primitive characters of subgroups of $M$-groups


Author: Mark L. Lewis
Journal: Proc. Amer. Math. Soc. 125 (1997), 27-33
MSC (1991): Primary 20C15
DOI: https://doi.org/10.1090/S0002-9939-97-03625-3
MathSciNet review: 1353389
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Abstract: Let $G$ be an $M$-group, let $S$ be a subnormal subgroup of $G$, and let $H$ be a Hall subgroup of $S$. If the character $\gamma \in \operatorname {Irr}(H)$ is primitive, then $\gamma (1)$ is a power of 2. Furthermore, if $|G:S|$ is odd, then $\gamma (1)=1$.


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Additional Information

Mark L. Lewis
Affiliation: Department of Mathematics, 400 Carver Hall, Iowa State University, Ames, Iowa 50011
Email: mllewis@iastate.edu

DOI: https://doi.org/10.1090/S0002-9939-97-03625-3
Received by editor(s): June 26, 1995
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1997 American Mathematical Society