Groups with ET0L co-word problem
Abstract
We study groups whose co-word problems are ET0L languages, which we call coET0L groups, using an automaton based model due to van Leeuwen, and recently studied by Bishop and Elder. In particular we prove a number of closure results for the class of groups with co-word problems in a subclass of `special' ET0L languages; that class of groups contains all groups that we know at the time of writing to be co-ET0L, including all groups that were proved by Holt and Röver to be stack groups, and hence co-indexed. It includes virtually free groups, bounded automata groups, and the Higman-Thompson groups, together with groups constructed from those using finitely generated subgroups, finite extension, free and direct products, and by taking the restricted standard wreath product of a co-\E group by a finitely generated virtually free top group.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.05323
- arXiv:
- arXiv:2408.05323
- Bibcode:
- 2024arXiv240805323A
- Keywords:
-
- Mathematics - Group Theory