A mixed identity-free elementary amenable group

Elementary Amenable Subgroups of R. Thompson's Group F

This paper contributes to the study of the subgroups of Thompson’s group F by constructing a sequence of subgroups of increasing complexity. The group F is an interesting finitely presented group with a pleasant, faithful representation in the group PLo(I) of orientation preserving, piecewise linear, self homeomorphisms of the unit interval. Thus our subgroups also lie in PLo(I). The subgroups ...

Non-elementary amenable subgroups of automata groups

We consider groups of automorphisms of locally finite trees, and give conditions on its subgroups that imply that they are not elementary amenable. This covers all known examples of groups that are not elementary amenable and act on the trees: groups of intermediate growths and Basilica group, by giving a more straightforward proof. Moreover, we deduce that all finitely generated branch groups ...

Lecture 5 : Examples of non - elementary amenable groups . The full topological group of Cantor minimal system

A Sofic Group Away from Amenable Groups

We give an example of a sofic group, which is not a limit of amenable groups.

An Amenable Group with a Nonsymmetric Group Algebra

Let G be a discrete group, h(G) the group algebra of G. Symmetry of h(G) has been considered in [l], [3]. Groups containing a free subgroup on two or more generators are the only groups found to have nonsymmetric group algebras, and in each case the groups found to have symmetric algebras are in the family of amenable groups. In this note we present an example of an amenable group with a nonsym...