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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Finite groups and the fixed points of coprime automorphisms


Author: Pavel Shumyatsky
Journal: Proc. Amer. Math. Soc. 129 (2001), 3479-3484
MSC (1991): Primary 20D45
Published electronically: April 25, 2001
MathSciNet review: 1860479
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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 $\vert A\vert\ge p^3$ and $C_G(a)$ is nilpotent of class at most $c$ for any $a\in A^\char93 $, then the group $G$ is nilpotent of $\{c,p\}$-bounded class.

2. If $\vert A\vert\ge p^4$ and $C_G(a)'$ is nilpotent of class at most $c$ for any $a\in A^\char93 $, then the derived group $G'$is nilpotent of $\{c,p\}$-bounded class.


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Additional Information

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

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06125-1
PII: S 0002-9939(01)06125-1
Keywords: Automorphisms, centralizers, associated Lie rings
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
Article copyright: © Copyright 2001 American Mathematical Society