Random subgroups of Thompson’s group F

Cleary, Sean and Elder, Murray and Rechnitzer, Andrew and Taback, Jennifer (2010) Random subgroups of Thompson’s group F. Groups, Geometry, and Dynamics . pp. 91-126. ISSN 1661-7207

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    We consider random subgroups of Thompson's group F with respect to two natural strati�cations of the set of all k generator subgroups. We �nd that the isomorphism classes of subgroups which occur with positive density are not the same for the two strati�cations. We give the �rst known exam- ples of persistent subgroups, whose isomorphism classes occur with positive density within the set of k-generator subgroups, for all su�ciently large k. Additionally, Thompson's group provides the �rst example of a group with- out a generic isomorphism class of subgroup. Elements of F are represented uniquely by reduced pairs of �nite rooted binary trees. We compute the asymptotic growth rate and a generating function for the number of reduced pairs of trees, which we show is D-�nite and not algebraic. We then use the asymptotic growth to prove our density results.

    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: 17 Sep 2012 10:43

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