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Transactions of the American Mathematical Society

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Positive laws in fixed points


Author: Pavel Shumyatsky
Journal: Trans. Amer. Math. Soc. 356 (2004), 2081-2091
MSC (2000): Primary 20D45
DOI: https://doi.org/10.1090/S0002-9947-03-03384-1
Published electronically: November 12, 2003
MathSciNet review: 2031054
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Abstract: Let $A$ be an elementary abelian group of order at least $q^3$ acting on a finite $q'$-group $G$in such a manner that $C_G(a)$ satisfies a positive law of degree $n$ for any $a\in A^\char93 $. It is proved that the entire group $G$ satisfies a positive law of degree bounded by a function of $q$ and $n$ only.


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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: https://doi.org/10.1090/S0002-9947-03-03384-1
Keywords: Automorphisms, centralizers, associated Lie rings
Received by editor(s): January 2, 2003
Received by editor(s) in revised form: April 15, 2003
Published electronically: November 12, 2003
Additional Notes: The author was supported by CNPq-Brazil
Article copyright: © Copyright 2003 American Mathematical Society

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