具有循环中心因子升列的群

Groups with an ascending series whose factors are cyclic and central

广义幂零群理论是无限群论理论的重要组成部分,受到国内外很多学者的关注.作者借助群的(超限)上中心列的构造,引入了超幂零群的定义,研究了超幂零群的基本性质,证明了在非有限生成群中群的超幂零性与幂零性是不等价的.同时还给出超限上中心群的一个特征性质.

The theory of generalized nilpotent groups is an important part of the theory of infinite groups, which is concerned by many domestic and foreign scholars. Here, the definition of supernilpo tent groups is introduced by means of the structure of hypercentral series of groups and their elementary properties are studied. It is shown that supernilpotence and nilpotence are not equivalent in non-finitely generated groups. Also, a characterization of hypercentral groups is given.