# Questions tagged [sofic-groups]

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9
questions

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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, ...

**3**

votes

**1**answer

174 views

### 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 ...

**7**

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**1**answer

391 views

### 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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325 views

### 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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**0**answers

277 views

### 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 ...

**3**

votes

**1**answer

298 views

### 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 $ba=0$?
...

**5**

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340 views

### 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|< ...

**5**

votes

**2**answers

979 views

### 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 ...

**21**

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**2**answers

2k views

### 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 $\...