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Star-free geodesic languages for groups

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.

Publication metadata

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.


DOI: 10.1142/S0218196707003603


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