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Star-free geodesic languages for groups
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Hermiller, Susan, Holt, Derek F. and Rees, Sarah (2007) Star-free geodesic languages for groups. International Journal of Algebra and Computation, Vol.17 (No.2). pp. 329-345. doi:10.1142/S0218196707003603 ISSN 0218-1967.
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Official URL: http://dx.doi.org/10.1142/S0218196707003603
Abstract
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.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | International Journal of Algebra and Computation | ||||
Publisher: | World Scientific Publishing Co. Pte. Ltd. | ||||
ISSN: | 0218-1967 | ||||
Official Date: | March 2007 | ||||
Dates: |
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Volume: | Vol.17 | ||||
Number: | No.2 | ||||
Number of Pages: | 17 | ||||
Page Range: | pp. 329-345 | ||||
DOI: | 10.1142/S0218196707003603 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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