Finite $p$-groups in which the normalizer of each nonnormal subgroup is small

Year 2024, Volume: 53 Issue: 6, 1642 - 1646, 28.12.2024

Libo Zhao Yangming Li Lü Gong , Xiuyun Guo

https://doi.org/10.15672/hujms.1362734

Abstract

Let $G$ be a finite non-Dedekindian $p$-group which satisfies $N_G(H)=HZ(G)$ for each nonnormal subgroup $H$, and we call it an $NS$-group. In this paper, it is proved that an $NS$-group is the product of a minimal nonabelian group and the center.

Keywords

non-Dedekindian $p$-group, the center, nonnormal subgroup

Project Number

The National Science Foundation of China (No. 12101135, 12071092,12371021, 12171302)

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