Vertices for characters of $p$-solvable groups
Author:
Gabriel Navarro
Journal:
Trans. Amer. Math. Soc. 354 (2002), 2759-2773
MSC (2000):
Primary 20C15
DOI:
https://doi.org/10.1090/S0002-9947-02-02974-4
Published electronically:
March 14, 2002
MathSciNet review:
1895202
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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
Article copyright:
© Copyright 2002
American Mathematical Society