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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Vertices for characters of $p$-solvable groups
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by Gabriel Navarro PDF
Trans. Amer. Math. Soc. 354 (2002), 2759-2773 Request permission

Abstract:

Suppose that $G$ is a finite $p$-solvable group. We associate to every irreducible complex character $\chi \in \operatorname {Irr}(G)$ of $G$ a canonical pair $(Q,\delta )$, where $Q$ is a $p$-subgroup of $G$ and $\delta \in \operatorname {Irr}(Q)$, uniquely determined by $\chi$ up to $G$-conjugacy. This pair behaves as a Green vertex and partitions $\operatorname {Irr}(G)$ into “families" of characters. Using the pair $(Q, \delta )$, we give a canonical choice of a certain $p$-radical subgroup $R$ of $G$ and a character $\eta \in \operatorname {Irr}(R)$ associated to $\chi$ which was predicted by some conjecture of G. R. Robinson.
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Additional Information
  • Gabriel Navarro
  • Affiliation: Departament d’Àlgebra, Facultat de Matemàtiques, Universitat de València, 46100 Burjassot. València, Spain
  • MR Author ID: 129760
  • Email: gabriel@uv.es
  • Received by editor(s): March 10, 2001
  • Received by editor(s) in revised form: October 10, 2001
  • Published electronically: March 14, 2002
  • Additional Notes: Research partially supported by DGICYT and MEC
  • © Copyright 2002 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 354 (2002), 2759-2773
  • MSC (2000): Primary 20C15
  • DOI: https://doi.org/10.1090/S0002-9947-02-02974-4
  • MathSciNet review: 1895202