Fitting subgroup and nilpotent residual of fixed points

Abstract

Let $q$ be a prime and $A$ an elementary abelian group of order at least $q^3$ acting by automorphisms on a finite $q^{\prime }$-group $G$. It is proved that if $|{\gamma }_{\infty }(C_G(a))|\le m$ for any $a\in A^{\#}$, then the order of ${\gamma }_{\infty }(G)$ is $m$-bounded. If $F(C_G(a))$ has index at most $m$ in $C_G(a)$ for any $a\in A^{\#}$, then the index of $F_2(G)$ is $m$-bounded.

arXiv admin note: text overlap with arXiv:1712.08103