The power structure of locally nilpotent \(\varvec{p}\) -groups

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• 作者：Heng Lv ; Guiyun Chen ; Wei Zhou
• 关键词：\(\check{\mathrm{C}}\) ; ernikov group ; Locally nilpotent group ; Divisible abelian p ; group
• 刊名：Archiv der Mathematik
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：108
• 期：2
• 页码：123-131
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1420-8938
• 卷排序：108

文摘

We shall extend the research on power structure of finite p-groups in Mann (J Algebra 42:121–135, 1976) to locally nilpotentp-groups. Firstly, we obtain that a locally nilpotent \(P_i\)-group G with \(|G:\mho _1(G)|< \infty \) is an extension of a divisible abelian group by a finite p-group. Next we get the structure of infinite locally nilpotent p-groups which are not \(P_i\)-groups, but all of whose proper infinite subgroups are \(P_i\)-groups. Finally, we show that locally nilpotent \(P_i\)-groups with all subgroups subnormal are nilpotent.