Questions tagged [sofic-groups]
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12 questions
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Amplification argument for hyperlinear groups
Let us define a group $G$ to be a hyperlinear group if it satisfies the conclusion of Theorem 3.6. in these notes by Vladimir Pestov. It is well-known that one can use the so-called amplification ...
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How to prove that pseudo entropy and topological entropy are the same with only Markov inequality and continuity?
Let $(X,\rho)$ be a compact metric space and $f:X\to X$ a homeomorphism. We say $(x_1,\ldots,x_{n})\in X^n$ is a partial $n$ orbit if $f(x_i)=x_{i+1}$. Let $Sep_{\epsilon}(X,\rho_n)$ be the maximal ...
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Direct proof that free groups are sofic
I am looking for a reference (or a simple proof) of the fact that a free group is sofic. The preferred dynamical definition of a sofic group seems to be that
there is a sequence of finite sets $V_n$ ...
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Uniform versus non-uniform group stability
Group stability considers the question of whether "almost"-homomorphisms are "close to" true homomorphisms. Here, "almost" and "close to" are made rigorous using a group metric.
More precisely, ...
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Is it possible to put Higman group as an amenable by sofic group?
I know Higman group has an amalgamated product decomposition of $BS(1, 2)$. Is it possible to decompose Higman group as some groups we are more familiar with. For example, is there a normal subgroup K ...
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Non-residually-finite finitely-presented sofic group with all finitely generated subgroups Hopfian
Is there a finitely presented sofic group which is not residually finite, but all of its finitely generated subgroups are Hopf groups?
It seems like the Baumslag Solitar groups $BS(m,n)$ don't work (...
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Other than the Higman group, what other candidates do we have for non-sofic groups?
I know that the Higman group is the most widely studied candidate right now, but what are the others? For example, is (are) Thompson's group(s) sofic? And what about the Burger-Mozes groups? I haven't ...
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Which conjectures are proved for sofic groups? [closed]
Which conjectures about groups are resolved in case of sofic groups?
I know two examples:
Kaplansky's direct finiteness conjecture (proved by Gabor Elek).
Some versions of Ornstein's isomorphism ...
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Group ring and left zero divisor II
Let $K$ be a finite field and $G$ be a discrete group.
Is it true that for every $a=e+a_1+\ldots+a_n,b=e+b_1+\ldots+b_m\in K[G]$ with $b_i\neq e,a_j\neq e$ the condition $ab=0$ implies $ba=0$?
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Zipper action of a discrete group.
A discrete group $\Gamma$ has zipper action if there is a set $X$ and an action of $\Gamma$ on $X$ (say left-action) and a subset $Z\subseteq X$ such that
for every $g \in \Gamma$: $|gZ\Delta Z|< ...
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Is Deligne's central extension sofic?
In P. Deligne. Extensions centrales non résiduellement finies de groupes
arithmétiques. CR Acad. Sci. Paris, série A-B, 287, 203–208, 1978. Deligne proves the existence of a certain central extension ...
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Properties of a non-sofic group
This question is, essentially, a comment of Mark Sapir. I think it deserves to be a question.
A countable, discrete group $\Gamma$ is sofic if for every $\epsilon>0$ and finite subset $F$ of $\...
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