The word problem of the Brin-Higman-Thompson groups

2020/06/26 by Birget, J. C.
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2006.14968

Abstract

We show that the word problem of the Brin-Higman-Thompson group n G_k,1 is \sf coNP-complete for all n ≥ 2 and all k ≥ 2. For this we prove that n G_k,1 is finitely generated, and that n G_k,1 contains a subgroup of 2 G_2,1 that can represent bijective circuits. We also show that for all n ≥ 1 and k ≥ 2: If K = 1 + (k-1) N for some N ≥ 1, then n G_K,1 ≤ n G_k,1. In particular, n G_K,1 ≤ n G_2,1 for all K ≥ 2.

Related

• The word problem of the Brin-Thompson group is coNP-complete
• Circuits, coNP-completeness, and the groups of Richard Thompson
• A monoid version of the Brin-Higman-Thompson groups
• Factorizations of the Thompson-Higman groups, and circuit complexity
• Progress around the Boone-Higman Conjecture