Groups with et0l co-word problem

We study groups whose co-word problems are et0l languages, which we call co-et0l 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 coword 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 extensions, free and direct products, and by taking the restricted standard wreath product of a co-et0l group by a finitely generated virtually free top group.