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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Character degrees and local subgroups
of $\pi $-separable groups


Authors: Gabriel Navarro and Thomas Wolf
Journal: Proc. Amer. Math. Soc. 126 (1998), 2599-2605
MSC (1991): Primary 20C15
MathSciNet review: 1458256
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $G$ be a finite $\{p,q \}$-solvable group for different primes $p$ and $q$. Let $P \in \text{Syl}_{p}(G)$ and $Q \in \text{Syl}_{q}(G)$ be such that $PQ=QP$. We prove that every $\chi \in \text{Irr}(G)$ of $p^{\prime }$-degree has $q^{\prime }$-degree if and only if $\mathbf{N}_{G}(P) \subseteq \mathbf{N}_{G}(Q)$ and $\mathbf{C}_{Q^{\prime }}(P)=1$.


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Additional Information

Gabriel Navarro
Affiliation: Departament d’Algebra, Facultat de Matemátiques, Universitat de València, 46100 Burjassot, València, Spain
Email: gabriel@uv.es

Thomas Wolf
Affiliation: Department of Mathematics, Ohio University, Athens, Ohio 45701
Email: wolf@bing.math.ohiou.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04507-9
PII: S 0002-9939(98)04507-9
Received by editor(s): February 13, 1997
Additional Notes: The first author is partially supported by DGICYT
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1998 American Mathematical Society