Finite groups and their coprime automorphisms
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- by Emerson de Melo and Pavel Shumyatsky PDF
- Proc. Amer. Math. Soc. 145 (2017), 3755-3760 Request permission
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 $a\in A^{\#}$. It is shown that $G$ is nilpotent with class bounded solely in terms of $c$ and $p$.References
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Additional Information
- Emerson de Melo
- Affiliation: Department of Mathematics, University of Brasília, Brasília-DF, 70910-900, Brazil
- MR Author ID: 983855
- Email: emerson@mat.unb.br
- Pavel Shumyatsky
- Affiliation: Department of Mathematics, University of Brasília, Brasília-DF, 70910-900, Brazil
- MR Author ID: 250501
- Email: pavel@unb.br
- 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
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 3755-3760
- MSC (2010): Primary 20D45
- DOI: https://doi.org/10.1090/proc/13550
- MathSciNet review: 3665030