Random subgroups of Thompson’s group F
نویسندگان
چکیده
We consider random subgroups of Thompson’s group F with respect to two natural stratifications of the set of all k generator subgroups of this group. We find that the isomorphism classes of subgroups which occur with positive density vary greatly between the two stratifications. We give the first known examples of persistent subgroups, whose isomorphism classes occur with positive density within the set of k-generator subgroups, for all k greater than some k0. Additionally, Thompson’s group provides the first example of a group without a generic isomorphism class of subgroup. In F , there are many isomorphism classes of subgroups with positive density less than one. Elements of F are represented uniquely by reduced pairs of ∗The first, second and fourth authors received support from a Bowdoin College Faculty Research Award. The first author acknowledges support from a PSC-CUNY Research Award. The third author thanks NSERC of Canada for financial support. The fourth author acknowledges support from NSF grant DMS-0437481. †Corresponding author
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