The word problem of the Brin-Thompson groups is coNP-complete

02/11/2019

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by   J. C. Birget, et al.

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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 n V 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.