## Inductive McKay condition for finite simple groups of type $\mathsf {C}$

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- by Marc Cabanes and Britta Späth
- Represent. Theory
**21**(2017), 61-81 - DOI: https://doi.org/10.1090/ert/497
- Published electronically: June 14, 2017
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## Abstract:

We verify the inductive McKay condition for simple groups of Lie type $\mathsf {C}$, namely finite projective symplectic groups. This contributes to the program of a complete proof of the McKay conjecture for all finite groups via the reduction theorem of Isaacs-Malle-Navarro and the classification of finite simple groups. In an important step we use a new counting argument to determine the stabilizers of irreducible characters of a finite symplectic group in its outer automorphism group. This is completed by analogous results on characters of normalizers of Sylow $d$-tori in those groups.## References

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## Bibliographic Information

**Marc Cabanes**- Affiliation: CNRS, IMJ-PRG, Boite 7012, 75205 Paris Cedex 13, France
- MR Author ID: 211320
- Email: marc.cabanes@imj-prg.fr
**Britta Späth**- Affiliation: Bergische Universität Wuppertal, Gaußstr. 20, 42119 Wuppertal, Germany
- Email: bspaeth@uni-wuppertal.de
- Received by editor(s): September 16, 2016
- Received by editor(s) in revised form: March 29, 2017
- Published electronically: June 14, 2017
- © Copyright 2017 American Mathematical Society
- Journal: Represent. Theory
**21**(2017), 61-81 - MSC (2010): Primary 20C15, 20C33; Secondary 20G40
- DOI: https://doi.org/10.1090/ert/497
- MathSciNet review: 3662374