Finite groups and the fixed points of coprime automorphisms
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- by Pavel Shumyatsky PDF
- Proc. Amer. Math. Soc. 129 (2001), 3479-3484 Request permission
Abstract:
Let $p$ be a prime, and let $G$ be a finite $p’$-group acted on by an elementary abelian $p$-group $A$. The following results are proved: 1. If $|A|\ge p^3$ and $C_G(a)$ is nilpotent of class at most $c$ for any $a\in A^\#$, then the group $G$ is nilpotent of $\{c,p\}$-bounded class. 2. If $|A|\ge p^4$ and $C_G(a)’$ is nilpotent of class at most $c$ for any $a\in A^\#$, then the derived group $G’$ is nilpotent of $\{c,p\}$-bounded class.References
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Additional Information
- Pavel Shumyatsky
- Affiliation: Department of Mathematics, University of Brasilia, Brasilia-DF, 70910-900 Brazil
- MR Author ID: 250501
- Email: pavel@ipe.mat.unb.br
- Received by editor(s): April 26, 2000
- Published electronically: April 25, 2001
- Additional Notes: The author was supported by CNPq-Brazil
- Communicated by: Stephen D. Smith
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 3479-3484
- MSC (1991): Primary 20D45
- DOI: https://doi.org/10.1090/S0002-9939-01-06125-1
- MathSciNet review: 1860479