This article combines the features of a survey and a research paper. It presents a review of
some results obtained during the last decade in problems related to the dynamics of branch …

A conjecture of Boone and Higman from the 1970's asserts that a finitely generated group $
G $ has solvable word problem if and only if $ G $ can be embedded into a finitely presented …

We present relations between growth, growth of diameters and the rate of vanishing of the
spectral gap in Schreier graphs of automaton groups. In particular, we introduce a series of …

We study asymptotic properties of chains of subgroups in residually finite groups using the
dynamics of boundary representations and the structure of periodic invariant measures on …

Nekrashevych associated to each self-similar group action an ample groupoid and a C*-
algebra. We provide exact sequences to compute the homology of the groupoid and the K …

arXiv:0803.3555v1 [math.GR] 25 Mar 2008 Page 1 arXiv:0803.3555v1 [math.GR] 25 Mar 2008
Classification of groups generated by 3-state automata over a 2-letter alphabet Ievgen …

arXiv:2308.05815v1 [math.GR] 10 Aug 2023 On exponentiation, p-automata and HNN
extensions of free abelian groups Page 1 arXiv:2308.05815v1 [math.GR] 10 Aug 2023 On …

(Free abelian)-by-free, self-similar groups generated by finite self-similar sets of tree
automorphisms and having unsolvable conjugacy problem are constructed. Along the way …

We canonically identify the groups of isometries and dilations of local fields and their rings of
integers with subgroups of the automorphism group of the $(d+ 1) $-regular tree $\widetilde …

Motivated by the renormalization method in statistical physics, Itai Benjamini defined a
finitely generated infinite group G to be scale-invariant if there is a nested sequence of finite …