少自同构的Cayley图:无限群的情况

Annales Henri Lebesgue Pub Date : 2020-10-12 DOI:10.5802/ahl.118

P. Leemann, M. Salle

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引用次数: 4

摘要

我们刻画了承认Cayley图且其唯一自同构是平移的有限生成群，证实了Watkins(1976)的一个猜想。这个证明依赖于随机游走技术。因此，每个有限生成群都存在一个具有可数自同构群的Cayley图。我们也处理有向图的情况。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Cayley graphs with few automorphisms: the case of infinite groups

We characterize the finitely generated groups that admit a Cayley graph whose only automorphisms are the translations, confirming a conjecture by Watkins from 1976. The proof relies on random walk techniques. As a consequence, every finitely generated group admits a Cayley graph with countable automorphism group. We also treat the case of directed graphs.

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Annales Henri Lebesgue

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