On Autonilpotent Finite Groups

2017/11/06 by Viachaslau I. Murashka, V. I. Murashka, Murashka, V. I.
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems #math.GR

paper · pdf · doi:10.48550/arxiv.1711.01688

arxiv created 2017/11/06 · openalex publication_date 2017/11/06 · arxiv updated 2017/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the paper autonilpotent groups were characterized as groups G such that AutG 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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