Context-free graphs and their transition groups
<|reference_start|>Context-free graphs and their transition groups: We define a new class of groups arising from context-free inverse graphs. We provide closure properties, prove that their co-word problems are context-free, study the torsion elements, and realize them as subgroups of the asynchronous rational group. Furthermore, we use a generalized version of the free product of graphs and prove that such a product is context-free inverse closed. We also exhibit an example of a group in our class that is not residually finite and one that is not poly-context-free. These properties make them interesting candidates to disprove both the Lehnert conjecture (which characterizes co-context-free groups as all subgroups of Thompson's group V) and the Brough conjecture (which characterizes finitely generated poly-context-free groups as virtual finitely generated subgroups of direct products of free groups).<|reference_end|>
@article{d'angeli2024context-free,
    title={Context-free graphs and their transition groups},
    author={Daniele D'Angeli, Francesco Matucci, Davide Perego, Emanuele Rodaro},
    journal={arXiv preprint arXiv:2408.13070},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.13070},
    primaryClass={math.GR cs.FL math.CO}
}