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Finite groups and their coprime automorphisms


Authors: Emerson de Melo and Pavel Shumyatsky
Journal: Proc. Amer. Math. Soc. 145 (2017), 3755-3760
MSC (2010): Primary 20D45
DOI: https://doi.org/10.1090/proc/13550
Published electronically: March 27, 2017
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Abstract: Let $ p$ be a prime and $ A$ a finite group of exponent $ p$ acting by automorphisms on a finite $ p'$-group $ G$. Assume that $ A$ has order at least $ p^3$ and $ C_G(a)$ is nilpotent of class at most $ c$ for any $ a\in A^{\char93 }$. It is shown that $ G$ is nilpotent with class bounded solely in terms of $ c$ and $ p$.


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Additional Information

Emerson de Melo
Affiliation: Department of Mathematics, University of Brasília, Brasília-DF, 70910-900, Brazil
Email: emerson@mat.unb.br

Pavel Shumyatsky
Affiliation: Department of Mathematics, University of Brasília, Brasília-DF, 70910-900, Brazil
Email: pavel@unb.br

DOI: https://doi.org/10.1090/proc/13550
Keywords: $p$-groups, automorphisms, fixed-point
Received by editor(s): June 3, 2016
Received by editor(s) in revised form: September 19, 2016, October 7, 2016, and October 12, 2016
Published electronically: March 27, 2017
Additional Notes: This research was supported by FAPDF and CNPq-Brazil
Communicated by: Pham Huu Tiep
Article copyright: © Copyright 2017 American Mathematical Society

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