Geodesic
Random subgroups of Thompson’s group $F$
Sean Cleary1 ; Murray Elder2 ; Andrew Rechnitzer3 ; Jennifer Taback4
1The City College of CUNY, New York, USA
2The University of Queensland, Brisbane, Australia
3The University of British Columbia, Vancouver, Canada
4Bowdoin College, Brunswick, USA
Groups, geometry, and dynamics, Tome 4 (2010) no. 1, pp. 91-126

Voir la notice de l'article provenant de la source EMS Press

DOI

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.
DOI : 10.4171/ggd/76
Classification : 05-XX, 20-XX, 00-XX
Mots-clés : Thompson's group <var>F</var>, asymptotic density, subgroup spectrum, visible subgroup, persistent subgroup, statistical group theory, asymptotic group theory, D-finite generating function, non-algebraic generating function

Sean Cleary  1   ; Murray Elder  2   ; Andrew Rechnitzer  3   ; Jennifer Taback  4

1 The City College of CUNY, New York, USA
2 The University of Queensland, Brisbane, Australia
3 The University of British Columbia, Vancouver, Canada
4 Bowdoin College, Brunswick, USA 
Sean Cleary; Murray Elder; Andrew Rechnitzer; Jennifer Taback. Random subgroups of Thompson’s group $F$. Groups, geometry, and dynamics, Tome 4 (2010) no. 1, pp. 91-126. doi: 10.4171/ggd/76
@article{10_4171_ggd_76,
     author = {Sean Cleary and Murray Elder and Andrew Rechnitzer and Jennifer Taback},
     title = {Random subgroups of {Thompson{\textquoteright}s} group $F$},
     journal = {Groups, geometry, and dynamics},
     pages = {91--126},
     year = {2010},
     volume = {4},
     number = {1},
     doi = {10.4171/ggd/76},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/76/}
}
TY  - JOUR
AU  - Sean Cleary
AU  - Murray Elder
AU  - Andrew Rechnitzer
AU  - Jennifer Taback
TI  - Random subgroups of Thompson’s group $F$
JO  - Groups, geometry, and dynamics
PY  - 2010
SP  - 91
EP  - 126
VL  - 4
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4171/ggd/76/
DO  - 10.4171/ggd/76
ID  - 10_4171_ggd_76
ER  - 
%0 Journal Article
%A Sean Cleary
%A Murray Elder
%A Andrew Rechnitzer
%A Jennifer Taback
%T Random subgroups of Thompson’s group $F$
%J Groups, geometry, and dynamics
%D 2010
%P 91-126
%V 4
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/76/
%R 10.4171/ggd/76
%F 10_4171_ggd_76

Cité par Sources :