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Groups with context-free co-word problem

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

Abstract

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

Topics: QA
Publisher: Cambridge University Press
Year: 2005
OAI identifier: oai:wrap.warwick.ac.uk:746

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