Finite groups and their coprime automorphisms

de Melo, Emerson; Shumyatsky, Pavel

doi:10.1090/proc/13550

Finite groups and their coprime automorphisms
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Proc. Amer. Math. Soc. 145 (2017), 3755-3760 Request permission

Abstract:

Let $p$ be a prime and $A$ a finite group of exponent $p$ acting by automorphisms on a finite $p’$-group $G$. Assume that $A$ has order at least $p^3$ and $C_G(a)$ is nilpotent of class at most $c$ for any $a\in A^{\#}$. It is shown that $G$ is nilpotent with class bounded solely in terms of $c$ and $p$.

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