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ON SUBGROUPS OF R. THOMPSON'S GROUP F.
- Source :
-
Transactions of the American Mathematical Society . Dec2017, Vol. 369, p8857-8878. 22p. - Publication Year :
- 2017
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 369
- Database :
- Academic Search Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 125614658
- Full Text :
- https://doi.org/10.1090/tran/6982