Groups with indexed co-word problem

by Derek Holt and Claas Röver

Keywords

word problems, indexed languages, automata groups, Higman-Thompson groups

Abstract

We investigate co-indexed groups, that is groups whose co-word problem (all words defining nontrivial elements) is an indexed language. We show that all Higman-Thompson groups and a large class of tree automorphism groups defined by finite automata are co-indexed groups. The latter class is closely related to dynamical systems and includes the Grigorchuk 2-group and the Gupta-Sidki 3-group. The co-word problems of all these examples are in fact accepted by nested stack automata with certain additional properties, and we establish various closure properties of this restricted class of co-indexed groups, incuding closure under free products.

This is published in in Internat. J. Algebra Comput. 16 (2006), no. 6, 985-1014

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