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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Character degrees and local subgroups of $\pi$-separable groups
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by Gabriel Navarro and Thomas Wolf PDF
Proc. Amer. Math. Soc. 126 (1998), 2599-2605 Request permission

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
  • MR Author ID: 129760
  • Email: gabriel@uv.es
  • Thomas Wolf
  • Affiliation: Department of Mathematics, Ohio University, Athens, Ohio 45701
  • Email: wolf@bing.math.ohiou.edu
  • Received by editor(s): February 13, 1997
  • Additional Notes: The first author is partially supported by DGICYT
  • Communicated by: Ronald M. Solomon
  • © Copyright 1998 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 126 (1998), 2599-2605
  • MSC (1991): Primary 20C15
  • DOI: https://doi.org/10.1090/S0002-9939-98-04507-9
  • MathSciNet review: 1458256