Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA non-LEA Sofic Group
144
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We describe elementary examples of finitely presented sofic groups which are not residually amenable (and thus not initially subamenable or LEA, for short). We ask if an amalgam of two amenable groups over a finite subgroup is residually amenable and answer this positively for some special cases, including countable locally finite groups, residually nilpotent groups and others.
rate research
Read More
Given a length function L on the R-modules of a unital ring R, for each sofic group $Gamma$ we define a mean length for every locally L-finite $RGamma$-module relative to a bigger $RGamma$-module. We establish an addition formula for the mean length. We give two applications. The first one shows that for any unital left Noetherian ring R, $RGamma$ is stably direct finite. The second one shows that for any $ZGamma$-module M, the mean topological dimension of the induced $Gamma$-action on the Pontryagin dual of M coincides with the von Neumann-L{u}ck rank of M.
We partially generalize Peters formula on modules over the group ring ${mathbb F} Gamma$ for a given finite field ${mathbb F}$ and a sofic group $Gamma$. It is also discussed that how the values of entropy are related to the zero divisor conjecture.
In this article we produce an example of a non-residually finite group which admits a uniformly proper action on a Gromov hyperbolic space.
We construct a finitely generated 2-dimensional group that acts properly on a locally finite CAT(0) cube complex but does not act properly on a finite dimensional CAT(0) cube complex.
We prove that the automorphism group of the braid group on four strands acts faithfully and geometrically on a CAT(0) 2-complex. This implies that the automorphism group of the free group of rank two acts faithfully and geometrically on a CAT(0) 2-complex, in contrast to the situation for rank three and above.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
