Related papers: Bireversible automata generating lamplighter group…

We study implications of expansiveness and pointwise periodicity for certain groups and semigroups of transformations. Among other things we prove that every pointwise periodic finitely generated group of cellular automata is necessarily…

We prove that the lamplighter group admits an injective Lipschitz map to any finitely generated metabelian group which is not virtually nilpotent. This implies that finitely generated metabelian groups satisfy the ``analytically…

The article presents several methods for the arithmetic of finite abelian groups. We introduce a tool - already used by Delsarte in [1] as I found out later - analogous to Dirichlet's convolution to obtain combinatorial results on these…

For every Turing machine, we construct an automaton group that simulates it. Precisely, starting from an initial configuration of the Turing machine, we explicitly construct an element of the group such that the Turing machine stops if, and…

A set is called recurrent if its minimal automaton is strongly connected and birecurrent if it is recurrent as well as its reversal. We prove a series of results concerning birecurrent sets. It is already known that any birecurrent set is…

We prove that the group of reversible cellular automata (RCA), on any alphabet $A$, contains a subgroup generated by three involutions which contains an isomorphic copy of every finitely generated group of RCA on any alphabet $B$. This…

We exhibit abelian topological groups admitting no nontrivial strongly continuous irreducible representations in Banach spaces. Among them are some abelian Banach-Lie groups and some monothetic subgroups of the unitary group of a separable…

We show that the group of bounded automatic automorphisms of a rooted tree is amenable, which implies amenability of numerous classes of groups generated by finite automata. The proof is based on reducing the problem to showing amenability…

We study natural linear representations of self-similar groups over finite fields. In particular, we show that if the group is generated by a finite automaton, then obtained matrices are automatic. This shows a new relation between two…

A group is metabelian if its commutator subgroup is abelian. For finitely generated metabelian groups, classical commutative algebra, algebraic geometry and geometric group theory, especially the latter two subjects, can be brought to bear…

For any infinite transitive sofic shift $X$ we construct a reversible cellular automaton (i.e. an automorphism of the shift $X$) which breaks any given finite point of the subshift into a finite collection of gliders traveling into opposing…

We classify the bireflections (products of 2 involutions) in the commutator subgroup G an orthogonal group O(V) over a finite field GF(q) of characteristic not 2. We show that every element of G is a bireflection if it is reversible…

(withdrawn.) For every lambda we give an explicit construction of an Abelian group with no non-trivial automorphisms. In particular the group absolutely has no non-trivial automorphisms, hence is absolutely indecomposable. Earlier we knew a…

We give sufficient conditions for when groups generated by automata in a class $\mathcal{C}$ of transducers, which contains the class of reset automata transducers, have infinite order. As a consequence we also demonstrate that if a group…

In this paper we show that there exists an uncountable family of finitely generated simple groups with the same positive theory as any non-abelian free group. In particular, these simple groups have infinite $w$-verbal width for all…

We show that the Novikov-Shubin invariant of an element of the integral group ring of the lamplighter group Z_2 \wr Z can be irrational. This disproves a conjecture of Lott and Lueck. Furthermore we show that every positive real number is…

We present novel constructions concerning the homology of finitely generated groups. Each construction draws on ideas of Gilbert Baumslag. There is a finitely presented acyclic group $U$ such that $U$ has no proper subgroups of finite index…

In this paper we determine all finitely generated abelian groups which are varietal capable with respect to the variety of polynilpotent groups. This result is a vast generalization of the famous Baer's result about capability of finitely…

In this paper, we discuss about finite groups in which, CGH = NGH, for every abelian subgroup H of non prime power order. Also, we classify all such nilpotent and minimal non nilpotent groups.

We prove that topologically isomorphic linear cellular automaton shifts are algebraically isomorphic. Using this, we show that two distinct such shifts cannot be isomorphic. We conclude that the automorphism group of a linear cellular…