scholarly journals On subgroups of R. Thompson’s group $F$

2017 ◽  
Vol 369 (12) ◽  
pp. 8857-8878 ◽  
Author(s):  
Gili Golan ◽  
Mark Sapir
Keyword(s):  
Thompson’S Group ◽  
Thompson's Group F

Thompson’s Group F

2018 ◽  
pp. 37-66
Author(s):  
Marianna C. Bonanome ◽  
Margaret H. Dean ◽  
Judith Putnam Dean
Keyword(s):  
Thompson’S Group ◽  
Thompson's Group F

scholarly journals ON THE PROPERTIES OF THE CAYLEY GRAPH OF RICHARD THOMPSON'S GROUP F

2004 ◽  
Vol 14 (05n06) ◽  
pp. 677-702 ◽  
Author(s):  
V. S. GUBA
Keyword(s):  
Growth Rate ◽  
Lower Bound ◽  
Cayley Graph ◽  
Upper Bound ◽  
Growth Function ◽  
Vertex Degree ◽  
General Growth ◽  
Thompson’S Group ◽  
Average Vertex ◽  
Thompson's Group F

We study some properties of the Cayley graph of R. Thompson's group F in generators x0, x1. We show that the density of this graph, that is, the least upper bound of the average vertex degree of its finite subgraphs is at least 3. It is known that a 2-generated group is not amenable if and only if the density of the corresponding Cayley graph is strictly less than 4. It is well known this is also equivalent to the existence of a doubling function on the Cayley graph. This means there exists a mapping from the set of vertices into itself such that for some constant K>0, each vertex moves by a distance at most K and each vertex has at least two preimages. We show that the density of the Cayley graph of a 2-generated group does not exceed 3 if and only if the group satisfies the above condition with K=1. Besides, we give a very easy formula to find the length (norm) of a given element of F in generators x0, x1. This simplifies the algorithm by Fordham. The length formula may be useful for finding the general growth function of F in generators x0, x1 and the growth rate of this function. In this paper, we show that the growth rate of F has a lower bound of [Formula: see text].

scholarly journals Random subgroups of Thompson’s group F

2010 ◽  
pp. 91-126 ◽  
Author(s):  
Sean Cleary ◽  
Murray Elder ◽  
Andrew Rechnitzer ◽  
Jennifer Taback
Keyword(s):  
Thompson’S Group ◽  
Thompson's Group F

scholarly journals Counting elements and geodesics in Thompson's group F

2010 ◽  
Vol 324 (1) ◽  
pp. 102-121 ◽  
Author(s):  
Murray Elder ◽  
Éric Fusy ◽  
Andrew Rechnitzer
Keyword(s):  
Thompson’S Group ◽  
Thompson's Group F
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