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On Groups Whose Geodesic Growth is Polynomial

Bridson, Martin R. and Burillo, José and Elder, Murray and Šunić, Zoran (2012) On Groups Whose Geodesic Growth is Polynomial. International Journal of Algebra and Computation, 22 (05). p. 1250048. ISSN 0218-1967

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    Abstract

    This note records some observations concerning geodesic growth functions. If a nilpotent group is not virtually cyclic then it has exponential geodesic growth with respect to all finite generating sets. On the other hand, if a finitely generated group G has an element whose normal closure is abelian and of finite index, then G has a finite generating set with respect to which the geodesic growth is polynomial (this includes all virtually cyclic groups).

    Item Type: Article
    Subjects: 20-xx Group theory and generalizations
    Faculty: UNSPECIFIED
    Depositing User: Dr Murray Elder
    Date Deposited: 17 Sep 2012 10:43
    Last Modified: 24 Oct 2012 10:18
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/1064

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