## 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.## References

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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