论文标题
Abelian最小封闭的局部紧凑型第二组的闭合正常亚组的分类
A classification of the abelian minimal closed normal subgroups of locally compact second-countable groups
论文作者
论文摘要
我们将本地紧凑的第二计数（L.C.S.C.）组分类为Abelian且拓扑特征的$ A $。所有此类组$ a $作为某些可溶性L.C.S.C.的整体发生。 $ g $的派生长度最多$ 3 $;除了已知的例外（具体来说，当$ a $是$ \ mathbb {q}^n $或其对\ in \ mathbb {n} $的$ n \）的双重偶尔时，我们可以将$ g $紧凑地生成。这相当于对L.C.S.C. Abelian主要因素的同构类型的分类。组，这对于紧凑的局部紧凑型组的理论特别感兴趣。
We classify the locally compact second-countable (l.c.s.c.) groups $A$ that are abelian and topologically characteristically simple. All such groups $A$ occur as the monolith of some soluble l.c.s.c. group $G$ of derived length at most $3$; with known exceptions (specifically, when $A$ is $\mathbb{Q}^n$ or its dual for some $n \in \mathbb{N}$), we can take $G$ to be compactly generated. This amounts to a classification of the possible isomorphism types of abelian chief factors of l.c.s.c. groups, which is of particular interest for the theory of compactly generated locally compact groups.
