A note on groups paralyzing a subgroup series
We consider groups $\Gamma$ of automorphisms of a group $G$ acting
by means of power automorphisms on the factors of a normal series in $G$ with
length $m$. We show that $[G, \Gamma]$ is nilpotent with class at most
$m$ and that this bound is best possible.
Moreover, such a $\Gamma$ is parasoluble with paraheight at
most $\frac{1}{2}m(m+3)+1$, provided $\Gamma'$ is periodic.
We give best possible bound in the case where the series is a central one.