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Groups with context-free co-word problem

Lookup NU author(s): Professor Sarah Rees



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.

Publication metadata

Author(s): Holt DF, Rees SE, Röver CE, Thomas RM

Publication type: Article

Publication status: Published

Journal: Journal of the London Mathematical Society

Year: 2005

Volume: 71

Issue: 3

Pages: 643-657

Print publication date: 01/06/2005

Date deposited: 25/01/2008

ISSN (print): 0024-6107

ISSN (electronic): 1469-7750

Publisher: Oxford University Press


DOI: 10.1112/S002461070500654X


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