摘要
l 群G称为紧生成的 ,如果对于G的任意子集 {aλ|λ∈Λ}且a =∨λ∈Λaλ 存在 ,必存在 {aλ|λ∈Λ}的有限子集a1、a2 ……an,使得a =∨ni=1 ai.主要结果是 :G∈F ,则G是紧生成的当且仅当G的任一个l 子群是闭的 ,且Γ(G)满足极小条件 .
An l group G is said to be compactly generated if for each subset {a λ|λ∈Λ} of G for which a=∨λ∈Λa λ exists,there exists a finite subset a 1,a 2,...,a n of {a λ|λ∈Λ} so that a=∨ni=1a i. The main result of this paper is as following: G∈F , G is compactly generated if and only if each l subgroup of G is closed and Γ(G) satisfies minimal condition.
出处
《商丘师范学院学报》
CAS
2001年第6期53-54,共2页
Journal of Shangqiu Normal University
关键词
紧生成l-群
离散l-群
极小条件
compactly generated l group
discrete l group
minimal condition
