On subgroups of R. Thompson’s group F

Gili Golan, Mark Sapir

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

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 >H1 > H2 > ··· such that ∩Hi = {1} and for every i there exist only finitely many subgroups of F containing Hi.

Original languageEnglish
Pages (from-to)8857-8878
Number of pages22
JournalTransactions of the American Mathematical Society
Volume369
Issue number12
DOIs
StatePublished - 1 Dec 2017
Externally publishedYes

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