Groups with context -free co-word problem

• Autores: Derek F. Holt, Sarah Rees , Class E. Röver, Richard M. Thomas
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 71, Nº 3, 2005, págs. 643-657
• Idioma: inglés
• DOI: 10.1112/s002461070500654x
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• Resumen

  • The class of co-context-free groups is studied. A co-context-free group is defined as one whose co-word problem (the complement of its word problem) is context-free. This class is larger than the subclass of context-free groups, being closed under the taking of finite direct products, restricted standard wreath products with context-free top groups, and passing to finitely generated subgroups and finite index overgroups. No other examples of co-context-free groups are known. It is proved that the only examples amongst polycyclic groups or the Baumslag-Solitar groups are virtually abelian. This is done by proving that languages with certain purely arithmetical properties cannot be context-free; this result may be of independent interest.