Powerful 2-Engel Groups

被引：6

作者：

Moravec, Primoz ^{[2
]}

Traustason, Gunnar ^{[1
]}

机构：

[1] Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon, England

[2] Oddelek Matemat, Inst Math Phys & Mech, Ljubljana, Slovenia

来源：

COMMUNICATIONS IN ALGEBRA | 2008年 / 36卷 / 11期

关键词：

2-Engel; Group; Powerful;

D O I：

10.1080/00927870802174835

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study powerful 2-Engel groups. We show that every powerful 2-Engel group generated by three elements is nilpotent of class at most two. Surprisingly, the result does not hold when the number of generators is larger than three. In this article and its sequel, we classify powerful 2-Engel groups of class 3 that are minimal in the sense that every proper powerful section is nilpotent of class at most 2.

引用

页码：4096 / 4119

页数：24

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