On a Class of Automata Groups Generalizing Lamplighter Groups
On a Class of Automata Groups Generalizing Lamplighter Groups
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论一类推广点灯者群的自动机群
DOI：
10.1142/s0218196705002761
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
B. Steinberg
中科院分区：
文献类型：
--
作者：
Pedro V. Silva;B. Steinberg
我们研究由重置自动机产生的自动机群。每一个点灯人群（n /n）都可以由这样一个自动机生成，一般来说，这些自动机群在性质上与点灯人相似：它们是可服从的局部有限循环群；在温和可决条件下，由自动机生成的半群是自由的。考虑了抛物子群和分形性质。
We study automata groups generated by reset automata. Every lamplighter group ℤ/nℤ wr ℤ can be generated by such an automaton, and in general these automata groups are similar in nature to lamplighters: they are amenable locally-finite-by-cyclic groups; under mild decidable conditions, the semigroups generated by such automata are free. Parabolic subgroups and fractal properties are considered.