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Lookup NU author(s): Professor Sarah Rees
In this article we show that every group with a finite presentation satisfying one or both of the small cancellation conditions C′(1/6) and C′(1/4) - T(4) has the property that the set of all geodesics (over the same generating set) is a star-free regular language. Star-free regularity of the geodesic set is shown to be dependent on the generating set chosen, even for free groups. We also show that the class of groups whose geodesic sets are star-free with respect to some generating set is closed under taking graph (and hence free and direct) products, and includes all virtually abelian groups. © World Scientific Publishing Company.
Author(s): Hermiller S, Holt DF, Rees S
Publication type: Article
Publication status: Published
Journal: International Journal of Algebra and Computation
Year: 2007
Volume: 17
Issue: 2
Pages: 329-345
Print publication date: 01/03/2007
ISSN (print): 0218-1967
ISSN (electronic): 1793-6500
Publisher: World Scientific Publishing Co. Pte. Ltd.
URL: http://dx.doi.org/10.1142/S0218196707003603
DOI: 10.1142/S0218196707003603
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