Subsets of groups with context-free preimages
| Autor: | Levine, Alex |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We study subsets $E$ of finitely generated groups where the set of all words over a given finite generating set that lie in $E$ forms a context-free language. We call these sets recognisably context-free. They are invariant of the choice of generating set and a theorem of Muller and Schupp fully classifies when the set $\{1\}$ can be recognisably context-free. We extend Muller and Schupp's result to show that a group $G$ admits a finite recognisably context-free subset if and only if $G$ is virtually free. We show that every conjugacy class of a group $G$ is recognisably context-free if and only if $G$ is virtually free. We conclude by showing that a coset is recognisably context-free if and only if the Schreier coset graph of the corresponding subgroup is quasi-isometric to a tree. Comment: 23 pages, 3 figures. Various corrections and removal of (former) Section 3 |
| Databáze: | arXiv |
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