We show that a compactly generated locally compact group of polynomial growth having no non-trivial compact normal subgroups can be embedded as a co-compact subgroup into a semidirect product of a connected, simply connected, nilpotent Lie group and a compact group. There is also a uniqueness statement for this extension.

中文翻译：

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关于具有多项式增长的群的结构 III

我们证明了一个紧凑生成的局部紧致多项式增长群，没有非平凡紧致正规子群，可以作为一个协同紧致子群嵌入到一个连通的、单连通的、幂零的李群和一个紧致群的半直积中。这个扩展还有一个唯一性声明。