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

IF 0.5 3区数学 Q3 MATHEMATICS

Journal of Algebra and Its Applications Pub Date : 2024-02-27 DOI:10.1142/s0219498825502020

Libo Zhao, Yangming Li, Lü Gong, Xiuyun Guo

引用次数: 0

Abstract

Let $G$ be a finite $p$ -group. Then $G$ is said to be a $C Z$ -group if $H_{G} \leq Z (G)$ for every nonnormal subgroup $H$ of $G$ . In this paper, we study the $C Z$ -group $G$ and get $c (G) \leq 3$ . It is proved that $exp (G^{'}) = p$ if $c (G) = 2$ and $| G | \leq p^{5}$ 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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来源期刊

Journal of Algebra and Its Applications 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

226

审稿时长

4-8 weeks

期刊介绍： The Journal of Algebra and Its Applications will publish papers both on theoretical and on applied aspects of Algebra. There is special interest in papers that point out innovative links between areas of Algebra and fields of application. As the field of Algebra continues to experience tremendous growth and diversification, we intend to provide the mathematical community with a central source for information on both the theoretical and the applied aspects of the discipline. While the journal will be primarily devoted to the publication of original research, extraordinary expository articles that encourage communication between algebraists and experts on areas of application as well as those presenting the state of the art on a given algebraic sub-discipline will be considered.