We prove that the word problem of the Brin-Thompson group nV over a finite generating set is coNP-complete for every n \ge 2. It is known that the groups nV are an infinite family of infinite, finitely presented, simple groups. We also prove that the word problem of the Thompson group V over a certain infinite set of generators, related to boolean circuits, is coNP-complete.

中文翻译：

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Brin-Thompson 群的单词问题是 coNP-complete

我们证明了有限生成集上的 Brin-Thompson 群 nV 的词问题对于每个 n \ge 2 都是 coNP 完全的。众所周知，群 nV 是无限的、有限呈现的简单群的无限族。我们还证明了与布尔电路相关的某个无限生成器集上的 Thompson 群 V 的词问题是 coNP 完全的。