Nilpotent residual of fixed points

Emerson de Melo, Aline de Souza Lima, Pavel Shumyatsky

Let $q$ be a prime and $A$ a finite $q$-group of exponent $q$ acting by automorphisms on a finite $q^{\prime }$-group $G$. Assume that $A$ has order at least $q^3$. We show that if $γ_{\inf…