Groups with ET0L co-word problem
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910030510424064 |
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| author | Kohli, Raad Al Holt, Derek F. Rees, Sarah |
| author_facet | Kohli, Raad Al Holt, Derek F. Rees, Sarah |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_05323 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Groups with ET0L co-word problem Kohli, Raad Al Holt, Derek F. Rees, Sarah Group Theory 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. |
| title | Groups with ET0L co-word problem |
| topic | Group Theory |
| url | https://arxiv.org/abs/2408.05323 |