We build presentations for automata groups generated by Cayley machines of finite groups of nilpotency class two and prove that these automata groups are all cross-wired lamplighter groups.

中文翻译：

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幂等二类群的凯莱机生成的自动机群

我们为由二类幂等有限群的 Cayley 机器生成的自动机群构建表示，并证明这些自动机群都是交叉连线的灯组。