The word problem of the Brin-Thompson group is coNP-complete
Abstract
We prove that the word problem of the Brin-Thompson group nV over a finite generating set is coNP-complete for every n 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.
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