A counter example for nilpotent groups

被引：0

作者：

Liu HeGuo ^{[1
]}

Zhang JiPing ^{[2
]}

Liao Jun ^{[2
]}

机构：

[1] Hubei Univ, Dept Math, Wuhan 430062, Peoples R China

[2] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2010年 / 53卷 / 11期

基金：

中国国家自然科学基金;

关键词：

nilpotency class; nilpotent group; nilpotent ring; Lie ring;

D O I：

10.1007/s11425-010-4116-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let R be a ring with 1, I be a nilpotent subring of R (there exists a natural number n, such that I(n) = 0), and I be generated by {x(j)vertical bar j is an element of J} as ring. Write U = 1 + I, and it is a nilpotent group with class <= n - 1. Let G be the subgroup of U which is generated by {1+x(j)vertical bar j is an element of J}. The group constructed in this paper indicates that the nilpotency class of G can be less than that of U.

引用

页码：3041 / 3048

页数：8