| Submitted exclusively to the London Mathematical Society DOI: 10.1112/S0000000000000000 GROUPS WITH CONTEXT-FREE CO-WORD PROBLEM (2008) | |||||||||||||
Abstract | |||||||||||||
| We study the class of co-context-free groups. We define a co-context-free group to be 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. But we do not know of other examples of co-context-free groups. We prove that the only examples amongst polycyclic groups or the Baumslag-Solitar groups are virtually abelian. We do this by proving that languages with certain purely arithmetical properties cannot be context-free; this result may be of independent interest. 1. | |||||||||||||
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