Positive laws in fixed points

Shumyatsky, Pavel

doi:10.1090/S0002-9947-03-03384-1

Positive laws in fixed points
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Trans. Amer. Math. Soc. 356 (2004), 2081-2091 Request permission

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.

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