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.

中文翻译：

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局部紧第二可数群的阿贝尔最小封闭正规子群的分类

我们对阿贝尔和拓扑特征简单的局部紧致第二可数 (lcsc) 群 $A$ 进行分类。所有这些基团 $A$ 都作为一些可溶的 lcsc 基团 $G$ 的整体出现，衍生长度最多为 $3$；除了已知的例外情况（特别是，当 $A$ 是 $\mathbb{Q}^n$ 或者它对某些 $n \in \mathbb{N}$ 的对偶时），我们可以将 $G$ 紧凑地生成。这相当于对 lcsc 群的阿贝尔主因子的可能同构类型的分类，这对于紧生成局部紧群的理论特别感兴趣。