A note on Engel words of finite groups

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• 作者：Huaquan Wei ; Liying Yang
• 关键词：Group ; Finite group ; Engel word ; Engel element ; p ; Nilpotent
• 刊名：Monatshefte f¨¹r Mathematik
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：181
• 期：4
• 页码：967-973
• 全文大小：368 KB
• 刊物主题：Mathematics, general;
• 出版者：Springer Vienna
• ISSN：1436-5081
• 卷排序：181

文摘

In this note, we introduce a generalisation of the concept of Engel elements called \(p'\)-Engel elements and investigate some basic properties of \(p'\)-Engel elements together with four related sets in a finite group. We obtain some characterisations of finite p-nilpotent groups, soluble groups and minimal non-p-nilpotent groups by use of \(p'\)-Engel elements.