A counter example for nilpotent groups  

作　　者：LIU HeGuo1, ZHANG JiPing2 & LIAO Jun2 1Department of Mathematics, Hubei University, Wuhan 430062, China 2School of Mathematical Sciences, Peking University, Beijing 100871, China 

出　　处：《Science China Mathematics》2010年第11期3041-3048,共8页中国科学：数学（英文版）

基　　金：supported by National Basic Research Program of China (Grant No. 2006CB805904);National Natural Science Foundation of China (Grant Nos. 10631010 and 10971054);Doctoral Foundation of Ministry of Education

摘　　要：Let R be a ring with 1, I be a nilpotent subring of R (there exists a natural number n, such that In = 0), and I be generated by {xj |j ∈ 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 + xj|j ∈ J}. The group constructed in this paper indicates that the nilpotency class of G can be less than that of U.Let R be a ring with 1, I be a nilpotent subring of R (there exists a natural number n, such that In = 0), and I be generated by {xj |j ∈ 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 + xj|j ∈ J}. The group constructed in this paper indicates that the nilpotency class of G can be less than that of U.

关 键 词：NILPOTENCY class NILPOTENT group NILPOTENT RING LIE RING 

分 类 号：O152.1[理学—数学]