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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Vertices for characters of $p$-solvable groups


Author: Gabriel Navarro
Journal: Trans. Amer. Math. Soc. 354 (2002), 2759-2773
MSC (2000): Primary 20C15
Published electronically: March 14, 2002
MathSciNet review: 1895202
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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
Email: gabriel@uv.es

DOI: http://dx.doi.org/10.1090/S0002-9947-02-02974-4
PII: S 0002-9947(02)02974-4
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