Finite p-groups in which the cores of all the nonnormal subgroups are in the center

Pub Date : 2024-02-27 DOI:10.1142/s0219498825502020
Libo Zhao, Yangming Li, Lü Gong, Xiuyun Guo
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Abstract

Let G be a finite p-group. Then G is said to be a CZ-group if HGZ(G) for every nonnormal subgroup H of G. In this paper, we study the CZ-group G and get c(G)3. It is proved that exp(G)=p if c(G)=2 and |G|p5 if c(G)=3.

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所有非正则子群的核心都在中心的有限 p 群
设 G 是有限 p 群。本文研究 CZ 群 G,得到 c(G)≤3。证明了当 c(G)=2 时,exp(G′)=p;当 c(G)=3 时,|G|≤p5。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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