Left 3-Engel elements in locally finite 2-groups

被引：1
|
作者：
Hadjievangelou, Anastasia [1 ]
Traustason, Gunnar [1 ]
机构：
[1] Univ Bath, Dept Math Sci, Bath, Avon, England
来源：
COMMUNICATIONS IN ALGEBRA | 2021年 / 49卷 / 11期
基金：
英国工程与自然科学研究理事会;
关键词：
Engel elements; Lie algebras; locally finite groups;
D O I：
10.1080/00927872.2021.1931265
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We give an infinite family of examples that generalize the construction given by Noce, Tracey and Traustason of a locally finite 2-group G containing a left 3-Engel element x where < x >(G), the normal closure of x in G, is not nilpotent. The construction is based on a family of Lie algebras that are of interest in their own right and make use of a classical theorem of Lucas, regarding when ((m)(n)) is even.
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页码：4869 / 4882
页数：14
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