## Positive laws in fixed points

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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 $a\in A^\#$. It is proved that the entire group $G$ satisfies a positive law of degree bounded by a function of $q$ and $n$ only.## 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): 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
- © Copyright 2003 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**356**(2004), 2081-2091 - MSC (2000): Primary 20D45
- DOI: https://doi.org/10.1090/S0002-9947-03-03384-1
- MathSciNet review: 2031054