Abstract

We introduce the notion of the metabelian rank of a group and study non-Abelian groups of finite metabelian rank. We prove the following result: If \(G \) is the extension of a locally finite group by a locally nilpotent-by-finite group and the metabelian rank of \(G \) is finite then the special rank of \(G \) is finite too.

中文翻译：

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有限阶变位阶的群类

摘要

我们介绍了一个组的metabelian级的概念，并研究了有限metabelian级的非阿贝尔组。我们证明以下结果：如果\（G \）是一个局部有限群的一个局部乘幂乘群，并且\（G \）的变位阶是有限的，那么\（G \ ）也是有限的。