Related papers: On elementary amenable bounded automata groups

Extensive amenability is a property of group actions which has recently been used as a tool to prove amenability of groups. We study this property and prove that it is preserved under a very general construction of semidirect products. As…

We prove that every linear-activity automaton group is amenable. The proof is based on showing that a sufficiently symmetric random walk on a specially constructed degree 1 automaton group -- the mother group -- has asymptotic entropy 0.…

We determine all finite p-groups that admit a faithful, self-similar action on the p-ary rooted tree such that the first level stabilizer is abelian. A group is in this class if and only if it is a split extension of an elementary abelian…

We introduce a wide class of countable groups, called properly proximal, which contains all non-amenable bi-exact groups, all non-elementary convergence groups, and all lattices in non-compact semi-simple Lie groups, but excludes all inner…

We classify the possible elementary amenable fundamental groups of compact aspherical 4-manifolds with boundary and conclude that they are either polycyclic or solvable Baumslag- Solitar. Since these groups are good and satisfy the…

We consider a finitely generated group acting minimally on a compact space by homeomorphsims, and assume that the Schreier graph of at least one orbit is quasi-isometric to a line. We show that the topological full group of such an action…

In this paper, we study some large scale properties of the mother groups of bounded automata groups. First we give two methods to prove every mother group has infinite asymptotic dimension. Then we study the decomposition complexity of…

For every natural number $n$, we classify abelian groups generated by an $n$-state time-varying automaton over the binary alphabet, as well as by an $n$-state Mealy automaton over the binary alphabet.

We study a class of finite groups $G$ which behave similarly to elementary abelian $p$-groups with $p$ prime, that is, there exists a subgroup $N$ such that all elements of $G\setminus N$ are conjugate or inverse-conjugate under $\Aut(G)$.…

The class A of countable groups that admit a faithful, transitive, amenable -- in the sense that there is an invariant mean -- action on a set has been widely investigated in the past. In this paper, we no longer require the action to be…

The paper has three parts. It is conjectured that for every elementary amenable group G and every non-zero commutative ring k, the homological dimension of G over k is equal to the Hirsch length of G whenever G has no k-torsion. In Part I…

We address the problem to characterise closed type I subgroups of the automorphism group of a tree. Even in the well-studied case of Burger-Mozes' universal groups, non-type I criteria were unknown. We prove that a huge class of groups…

We study infinite groups interpretable in power bounded $T$-convex, $V$-minimal or $p$-adically closed fields. We show that if $G$ is an interpretable definably semisimple group (i.e., has no definable infinite normal abelian subgroups)…

A central question in the theory of automata is which classes of automata can be minimized in polynomial time. We close the remaining gaps for deterministic and history-deterministic automata over infinite words by proving that…

We consider linear groups which do not contain unipotent elements of infinite order, which includes all linear groups in positive characteristic, and show that this class of groups has good properties which resemble those held by groups of…

We study the positive theory of groups acting on trees and show that under the presence of weak small cancellation elements, the positive theory of the group is trivial, i.e. coincides with the positive theory of a non-abelian free group.…

In this paper we extend the approach of M. Cavaleri to effective amenability to the class of computably enumerable groups, i.e. in particular we do not assume that groups are finitely generated. In the case of computable groups we also…

We give a classification of maximal elements of the set of finite groups that can be realized as the full automorphism groups of simple polarized abelian fourfolds over finite fields. As an application, we compute the Jordan constants of…

Finite groups with very few character values are characterized. The following is the main result of this article: a finite non-abelian group has precisely four character values if and only if it is the generalized dihedral group of a…

For every prime $p$ and integer $n\ge 3$ we explicitly construct an abelian variety $A/\F_{p^n}$ of dimension $n$ such that for a suitable prime $l$ the group of quasi-isogenies of $A/\F_{p^n}$ of $l$-power degree is canonically a dense…