Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

Request Permissions   Purchase Content 
 
 

 

On subgroups of R. Thompson's group $ F$


Authors: Gili Golan and Mark Sapir
Journal: Trans. Amer. Math. Soc. 369 (2017), 8857-8878
MSC (2010): Primary 20F65, 20G07
DOI: https://doi.org/10.1090/tran/6982
Published electronically: August 3, 2017
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We provide two ways to show that the R. Thompson group $ F$ has maximal subgroups of infinite index which do not fix any number in the unit interval under the natural action of $ F$ on $ (0,1)$, thus solving a problem by D. Savchuk. The first way employs Jones' subgroup of the R. Thompson group $ F$ and leads to an explicit finitely generated example. The second way employs directed 2-complexes and 2-dimensional analogs of Stallings' core graphs and gives many implicit examples. We also show that $ F$ has a decreasing sequence of finitely generated subgroups $ F>H_1>H_2>\cdots $ such that $ \cap H_i=\{1\}$ and for every $ i$ there exist only finitely many subgroups of $ F$ containing $ H_i$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 20F65, 20G07

Retrieve articles in all journals with MSC (2010): 20F65, 20G07


Additional Information

Gili Golan
Affiliation: Department of Mathematics, Bar-Ilan University, 5290002 Ramat-Gan, Israel

Mark Sapir
Affiliation: Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240

DOI: https://doi.org/10.1090/tran/6982
Received by editor(s): August 10, 2015
Received by editor(s) in revised form: October 14, 2015, and April 22, 2016
Published electronically: August 3, 2017
Additional Notes: This research was partially supported by the NSF grant DMS-1500180. The paper was written while the second author was visiting the Max Planck Institute for Mathematics in Bonn.
Article copyright: © Copyright 2017 American Mathematical Society