On Autonilpotent Finite Groups

In the paper autonilpotent groups were characterized as groups $G$ such that $\mathrm{A}\mathrm{u}\mathrm{t}G$ stabilizes some chain of subgroups of $G$. It was shown that a $p$-group is autonilpotent if and only if its group of automorphisms is also a $p$-group. Analogues of Baer’s theorem about the hypercenter and Frobenius $p$-nilpotency criterion were obtained for autonilpotent groups.