3 problems

Bounded Fitting-height subgroup conjecture. $G$ has a characteristic subgroup $H$ such that:

Uniform Fitting-height conjecture. For every $f(x)\in\mathbb{Z}[x]\setminus\{0\}$, there exist integers $k(f(x))>0$ and $m(f(x))$ such that, whenever $G$ is a finite solvable group…

Nilpotent fixed-point-free automorphism conjecture. If the action is fixed point free, equivalently $C_G(A)=1$, then