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A Brauer-Wielandt formula (with an application to character tables)


Authors: Gabriel Navarro and Noelia Rizo
Journal: Proc. Amer. Math. Soc. 144 (2016), 4199-4204
MSC (2010): Primary 20Dxx; Secondary 20C15
DOI: https://doi.org/10.1090/proc/13089
Published electronically: April 20, 2016
MathSciNet review: 3531172
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Abstract: If a $ p$-group $ P$ acts coprimely on a finite group $ G$, we give a Brauer-Wielandt formula to count the number of fixed points $ \vert {\bf C}_{G}(P) \vert$ of $ P$ in $ G$. This serves to determine the number of Sylow $ p$-subgroups of certain finite groups from their character tables.


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Additional Information

Gabriel Navarro
Affiliation: Departament d’Àlgebra, Universitat de València, 46100 Burjassot, València, Spain
Email: gabriel.navarro@uv.es

Noelia Rizo
Affiliation: Departament d’Àlgebra, Universitat de València, 46100 Burjassot, València, Spain
Email: noelia.rizo@uv.es

DOI: https://doi.org/10.1090/proc/13089
Keywords: Brauer-Wielandt, character tables
Received by editor(s): December 12, 2015
Received by editor(s) in revised form: December 13, 2015, and January 7, 2016
Published electronically: April 20, 2016
Additional Notes: The research of the first author was supported by the Prometeo/Generalitat Valenciana, and Proyecto MTM2013-40464-P. The second author was supported by a Fellowship FPU of Ministerio de Educación, Cultura y Deporte
Communicated by: Pham Huu Tiep
Article copyright: © Copyright 2016 American Mathematical Society

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