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arXiv · 1711.01688

On Autonilpotent Finite Groups

V. I. Murashka
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Abstract

In the paper autonilpotent groups were characterized as groups $G$ such that $\mathrm{Aut}G$ 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.

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V. I. Murashka. 2017-11-06. On Autonilpotent Finite Groups. https://arxiv.org/abs/1711.01688

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