We give a simple and unified proof showing that the unrestricted wreath product of a weakly sofic, sofic, linear sofic, or hyperlinear group by an amenable group is weakly sofic, sofic, linear sofic, or hyperlinear, ...

We consider a definition of entropy for discrete amenable action groups and extend the equality between enreopy and dimension for amenable groups. This last result was proved by Simpson for the special case of Z^d-actions

For every infinite (countable discrete) amenable group G and every positive integer d we construct a minimal G-action of mean dimension d/2 which cannot be embedded in the full G-shift on ([0,1](d))(G) .

The main results of this note extend a theorem of Kesten for symmetric random walks on discrete groups to group extensions of topological Markov chains. In contrast to the result in probability theory, there is a notable ...

Using ultrapowers of C-algebras, we provide a new construction of the multiplier algebra of a C-algebra. This extends the work of Avsec and Goldbring [Houston J. Math., to appear, arXiv:1610.09276] to the setting ...

We consider a set of necessary conditions which are efficient heuristics for deciding when a set of Wang tiles cannot tile a group. Piantadosi [19] gave a necessary and sufficient condition for the existence of a valid ...