Random subgroups of Thompson's group F

Cleary, Sean, Elder, Murray, Rechnitzer, Andrew and Taback, Jennifer (2010) Random subgroups of Thompson's group F. Groups, Geometry, and Dynamics, 4 1: 91-126. doi:10.4171/GGD/76

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Author Cleary, Sean
Elder, Murray
Rechnitzer, Andrew
Taback, Jennifer
Title Random subgroups of Thompson's group F
Journal name Groups, Geometry, and Dynamics   Check publisher's open access policy
ISSN 1661-7207
Publication date 2010
Sub-type Article (original research)
DOI 10.4171/GGD/76
Volume 4
Issue 1
Start page 91
End page 126
Total pages 36
Place of publication Zurich, Switzerland
Publisher European Mathematical Society Publishing House
Collection year 2011
Language eng
Subject 0105 Mathematical Physics
Formatted abstract
We consider random subgroups of Thompson’s group F with respect to two natural stratifications of the set of all k-generator subgroups. We find that the isomorphism classes of subgroups which occur with positive density are not the same for 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 sufficiently large k. Additionally, Thompson’s group provides the first example of a group without a generic isomorphism class of subgroup. Elements of F are represented uniquely by reduced pairs of finite 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-finite (short for differentiably finite) and not algebraic. We then use the asymptotic growth to prove our density results.
© European Mathematical Society.
Keyword Thompson's group F
Asymptotic density
Subgroup spectrum
Visible subgroup
Persistent subgroup
Statistical group theory
Asymptotic group theory
D-finite generating function
Non-algebraic generating function
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2011 Collection
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Citation counts: TR Web of Science Citation Count  Cited 4 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 5 times in Scopus Article | Citations
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Created: Sun, 13 Dec 2009, 00:05:59 EST