ON A TORSION-FREE WEAKLY BRANCH GROUP DEFINED BY A THREE STATE AUTOMATON
From MaRDI portal
Publication:4786318
DOI10.1142/S0218196702001000zbMath1070.20031MaRDI QIDQ4786318
Andrzej Żuk, Rostislav I. Grigorchuk
Publication date: 15 December 2002
Published in: International Journal of Algebra and Computation (Search for Journal in Brave)
growthamenabilityfractalnessbranchnessjust infinitenessthree-state automatatorsion free weakly branch groups
Sums of independent random variables; random walks (60G50) Generators, relations, and presentations of groups (20F05) Algebraic theory of languages and automata (68Q70) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Groups acting on trees (20E08)
Related Items (49)
Mapping schemes realizable by obstructed topological polynomials ⋮ Amenability and non-uniform growth of some directed automorphism groups of a rooted tree ⋮ Ergodic decomposition of group actions on rooted trees ⋮ PROFINITE COMPLETION OF GRIGORCHUK'S GROUP IS NOT FINITELY PRESENTED ⋮ Generalized Grigorchuk’s overgroups as points in the space of marked 8-generated groups ⋮ Piecewise automatic groups. ⋮ Galois groups of tamely ramified \(p\)-extensions ⋮ Automata, groups, limit spaces, and tilings. ⋮ Random Sampling of Trivial Words in Finitely Presented Groups ⋮ Exponential growth of some iterated monodromy groups ⋮ On amenability of automata groups. ⋮ Key agreement based on automaton groups ⋮ A finitely generated branch group of exponential growth without free subgroups. ⋮ On maximal subgroups of infinite index in branch and weakly branch groups ⋮ \(p\)-Basilica groups ⋮ The smallest Mealy automaton generating an indicable regular branch group ⋮ Non-elementary amenable subgroups of automata groups ⋮ On the simplicity of Nekrashevych algebras of contracting self-similar groups ⋮ A Thompson group for the basilica ⋮ Asymptotic behaviors of random walks on countable groups ⋮ On the Basilica operation ⋮ Behaviors of entropy on finitely generated groups ⋮ Introduction to iterated monodromy groups ⋮ Counting dimer coverings on self-similar Schreier graphs ⋮ Diameters, distortion, and eigenvalues ⋮ Some topics in the dynamics of group actions on rooted trees. ⋮ On a class of poly-context-free groups generated by automata ⋮ Pro-\(\mathcal {C}\) congruence properties for groups of rooted tree automorphisms ⋮ Automata generating free products of groups of order 2. ⋮ FINITE SELF-SIMILAR p-GROUPS WITH ABELIAN FIRST LEVEL STABILIZERS ⋮ Branch rings, thinned rings, tree enveloping rings. ⋮ Amenable groups without finitely presented amenable covers ⋮ The abelian sandpile model on randomly rooted graphs and self-similar groups ⋮ A NILPOTENT QUOTIENT ALGORITHM FOR CERTAIN INFINITELY PRESENTED GROUPS AND ITS APPLICATIONS ⋮ Equilibrium states on the Cuntz-Pimsner algebras of self-similar actions ⋮ Unnamed Item ⋮ From Self-Similar Groups to Self-Similar Sets and Spectra ⋮ Extensions of amenable groups by recurrent groupoids ⋮ Galois groups and Cantor actions ⋮ Boundary dynamics for bireversible and for contracting automaton groups ⋮ Wiener, edge-Wiener, and vertex-edge-Wiener index of Basilica graphs ⋮ Zeta functions of finite Schreier graphs and their zig-zag products ⋮ Connectedness and Isomorphism Properties of the Zig-Zag Product of Graphs ⋮ Graph automaton groups ⋮ Engel elements in some fractal groups ⋮ On simplicity of reduced C*-algebras of groups ⋮ SOLENOIDAL MAPS, AUTOMATIC SEQUENCES, VAN DER PUT SERIES, AND MEALY AUTOMATA ⋮ On elementary amenable bounded automata groups ⋮ Amenability via random walks.
Cites Work
- On the Burnside problem for periodic groups
- A just-nonsolvable torsion-free group defined on the binary tree
- On problems related to growth, entropy, and spectrum in group theory
- Sous-groupes paraboliques et représentations de groupes branchés
- Full Banach Mean Values on Countable groups.
- Spectra of non-commutative dynamical systems and graphs related to fractal groups
This page was built for publication: ON A TORSION-FREE WEAKLY BRANCH GROUP DEFINED BY A THREE STATE AUTOMATON
