Skip to main content
Article thumbnail
Location of Repository

Groups with a context-free co-word problem

By D. F. Holt, Sarah Rees, Claas E. Röver and Richard M. Thomas


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

Year: 2005
DOI identifier: 10.1112/S002461070500654X
OAI identifier:
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • (external link)
  • (external link)
  • Suggested articles

    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.