Elementary Classes of Groups
Elementary Classes of Groups
复制标题
团体初级班
DOI：
10.1023/a:1019869105364
复制
发表时间：
2002
影响因子：
0.6
通讯作者：
D. Osin
中科院分区：
文献类型：
--
作者：
D. Osin
摘要
设\(B\)是一类群。以\(B\)为基的初等类被定义为包含\(B\)且对子群、商群、群扩张以及正向极限封闭的最小的群类。研究了这类群的性质。考虑了其在初等顺从群理论中的一些应用以及与广义可解群的库罗什 - 切尔尼科夫类的一种关系。
AbstractLet
$$B$$
be a class of groups. The elementary class with base
$$B$$
is defined as the minimal class of groups containing
$$B$$
and closed with respect to taking subgroups, quotient groups, group extensions, and direct limits. Properties of such classes are studied. Some applications to the theory of elementary amenable groups and a relation to the Kurosh--Chernikov classes of generalized solvable groups are considered.