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

Year 2024, Early Access, 1 - 5

Lü Gong

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 $H$, we call it an $NS$-group.
In this paper, it is proved that an $NS$-group is the product of 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)

References

• [1] Y. Berkovich, Groups of Prime Power Order, volume 1, Walter de Gruyter, Berlin, 2008.