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Cone types and geodesic languages for lamplighter groups and Thompson's group F

Cleary, Sean and Elder, Murray and Taback, Jennifer (2006) Cone types and geodesic languages for lamplighter groups and Thompson's group F. Journal of Algebra, 303 (2). pp. 476-500. ISSN 00218693

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    Abstract

    We study languages of geodesics in lamplighter groups and Thompson’s group F. We show that the lamplighter groups Ln have infinitely many cone types, have no regular geodesic languages, and have 1-counter, context-free and counter geodesic languages with respect to certain generating sets. We show that the full language of geodesics with respect to one generating set for the lamplighter group is not counter but is context-free, while with respect to another generating set the full language of geodesics is counter and context-free. In Thompson’s group F with respect to the standard finite generating set, we show there are infinitely many cone types and that there is no regular language of geodesics. We show that the existence of families of “seesaw” elements with respect to a given generating set in a finitely generated infinite group precludes a regular language of geodesics and guarantees infinitely many cone types with respect to that generating set.

    Item Type: Article
    Subjects: 20-xx Group theory and generalizations
    Faculty: UNSPECIFIED
    Depositing User: Dr Murray Elder
    Date Deposited: 17 Sep 2012 10:41
    Last Modified: 17 Sep 2012 10:41
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/1073

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