Resumen de Groups with context -free co-word problem

Derek F. Holt, Sarah Rees , Class E. Röver, 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.