Questions tagged [amenability]
The amenability tag has no usage guidance.
160
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Finitely presented groups which are not residually amenable
What are examples of finitely presented but not residually amenable groups?
Well, the examples that I want to have are simple f.p. groups as well as examples of non residually amenable groups arise ...
6
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1
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a paradoxical decomposition of a group
Just my curiosity... Are there proofs the following fact, which does not involve Hall's matching theorem:
A group $\Gamma$ is amenable if and only if it does not admit a paradoxical decomposition.
...
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14
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Some questions on unitarisability of discrete groups
In this post I would like to ask several of questions related to Dixmier problem. I will try to make the post as self-contained as possible.
A discrete group $G$ is unitarisable if for every Hilbert ...
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When do isometric actions exist?
Let $X$ be a metrizable topological space and $G$ be a locally compact group. Given a continuous (left) action of $G$ on $X$, is there a metric on $X$, compatible with the topology, for which the ...
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Amenability of groups II
Are there any non-amenable group $G$ with the property:
There exists $C<1$ such that for every finite set $S\subset G$ there exists a set $F\subseteq S$ such that $|F|\geq C |S|$ and $F$ generates ...
- 4,695
15
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1
answer
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Amenable groups with finite classifying space
A group $G$ is said to be elementary amenable if it can be obtained from finite and abelian groups by subgroups, quotients, extensions and increasing unions. It is well-known that all such groups are ...
- 25.3k
15
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Amenability of groups in terms of a perturbation condition
Let $G$ be a countable group and $\lambda \colon G \to U(\ell^2 G)$ its left-regular representation. Suppose that there exists a constant $C>0$ such that for all $T \in B(\ell^2 G)$
$$\inf \lbrace\...
- 25.3k
2
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Characterizations of amenable groups which use the space $\ell_1(G)$ and convolution
Let $G$ be a discrete group.
Do you know characterizations of amenable groups which use the space $\ell_1(G)$ and convolution?
I only know Johnson's theorem:
A group is amenable if and only if the ...
21
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1
answer
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Amenability of groups
Let $G$ be non-amenable finitely generated group.
1) Is it true that there exists a sequence $S(n)$ of sets which generate $G$ and such that
$\frac{1}{|S(n)|}||\sum_{g\in S(n)} \lambda(g)||\...
- 4,695
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Is Thompson's Group F amenable?
Last year a paper on the arXiv (Akhmedov) claimed that Thompson's group $F$ is not amenable, while another paper, published in the journal "Infinite dimensional analysis, quantum probability, and ...
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