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Results tagged with gr.group-theory
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user 33828
Questions about the branch of algebra that deals with groups.
1
vote
Actions of Thompson group F. II
The answer to the question as stated is yes, there is no binary tree as a subgraph for the standard action with standard generators (but there is a binary tree for some generating set). It follows fro …
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2
votes
Rotation numbers for amenable group actions on the circle
I think the paper http://arxiv.org/abs/0910.0218 contains nice information related to the questions.
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4
votes
Accepted
Uniform bounds on Kazhdan constants in groups
The answer is yes, by Gelander and Zuk: http://www.ams.org/mathscinet/search/publdoc.html?pg1=INDI&s1=697297&vfpref=html&r=24&mx-pid=1910934
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5
votes
Actions of Thompson group F
$F$ is bi-orderable, so if you care about actions by homeomorphisms on the line, you can pick up a bi-ordering and produce a dynamical realization: a faithful almost free action ( see Proposition 3.4 …
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18
votes
Is there an infinite group with exactly two conjugacy classes?
As a psychological curiosity, Per Enflo writes in his Autobiography that the existence of groups with two conjugacy classes was a key insight behind his many solutions to outstanding problems in Funct …
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6
votes
1
answer
500
views
Partition of a group into small subsets
A nonempty subset $S$ of a group $G$ is called small if there is an infinite sequence of elements $g_n$ in $G$ such that the translated sets $g_nS$ are pairwise disjoint.
Question: Is there a group …
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7
votes
1
answer
653
views
Growth of Thompson's group $F$
EDIT(August 2013): I accepted Mark's answer as being the state of art- there are two relevant references, one in the answer and one in the comments. The minimal growth rate of $F$ remains unknown with …
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5
votes
Trees in groups of exponential growth
This (so nice) question seems to be equivalent with the notorious and old problem of constructing a supraamenable (or superamenable) group of exponential growth. Recall that a supraamenable group is o …
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15
votes
3
answers
2k
views
Folner sets and balls
Several related questions were asked before on MO, but it is not clear to me if the following was settled.
Given a finitely generated amenable group, is it always possible to find some finite genera …
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21
votes
3
answers
2k
views
The role of the Automatic Groups in the history of Geometric Group Theory
What is the role of the theory of Automatic Groups in the history of Geometric Group Theory?
Motivation:
When I read through the "Word Processing in Groups" I was amazed by the supreme beauty and el …
4
votes
Accepted
Speed of random walks in groups
For nilpotent groups the speed exponent is 0.5. See this paper for the general picture http://arxiv.org/abs/1203.6226 .
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16
votes
0
answers
435
views
Splay trees and Thompson's group $F$
( I apologize for only indicating some easy to find references, but new users are not allowed to link more than five). This is very speculative, but:
Question: Is there a reformulation of the Dynamic …
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