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Pro-\(\mathcal {C}\) congruence properties for groups of rooted tree automorphisms
We propose a generalisation of the congruence subgroup problem for groups acting on rooted trees. Instead of only comparing the profinite completion...
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On p-adic Colligations and ‘Rational Maps’ of Bruhat–Tits Trees
Consider matrices of order k+N over p-adic field determined up to conjugations by elements of GL(N) over p-adic integers. We define a product of such...
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The Surface Group Conjecture: Cyclically Pinched and Conjugacy Pinched One-Relator Groups
The general surface group conjecture asks whether a one-relator group where every subgroup of finite index is again one-relator and every subgroup of...
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Length functions of 2-dimensional right-angled Artin groups
Morgan and Culler proved that a minimal action of a free group on a tree is determined by its translation length function. We prove an analogue of...
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An algorithm to identify automorphisms which arise from self-induced interval exchange transformations
We give an algorithm to determine if the dynamical system generated by a positive automorphism of the free group can also be generated by a...
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Combinatorial \({\mathbb{R}}\)-trees as generalized Cayley graphs for fundamental groups of one-dimensional spaces
In their study of fundamental groups of one-dimensional path-connected compact metric spaces, Cannon and Conner have asked: Is there a tree-like...
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A Note on Lyndon Properties in One-Relator Groups
Lyndon (Combinatorial Group Theory,
1977 ) proved that in a free group F each solution set { x , y , z } of the quadratic equation x 2 y 2 z 2 = 1 generates... -
Pattern closure of groups of tree automorphisms
It is shown that every group of automorphisms of a regular rooted tree that is defined by forbidding a set of patterns of size s + 1 is the...
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Generating Sym(ω) by Permutations Preserving Dense Orders
We show how generic permutations of ω can be presented by products of permutations preserving dense orders.
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Finite generation of iterated wreath products
Let ( G n , X n ) be a sequence of finite transitive permutation groups with uniformly bounded number of generators. We prove that the infinitely...
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Simple locally compact groups acting on trees and their germs of automorphisms
Automorphism groups of locally finite trees provide a large class of examples of simple totally disconnected locally compact groups. It is desirable...
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Prographes sylvestres et groupes profinis presque libres
In this article we want to give an analogous in the profinite case to the following theorem: an abstract group is free if and only if it acts freely...
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Twin building lattices do not have asymptotic cut-points
We show that twin building lattices have linear divergence, which implies that all asymptotic cones are without cut-points.
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Random groups do not split
We prove that random groups in the Gromov density model, at any density, satisfy property (FA), i.e. they do not act non-trivially on simplicial...
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Normal origamis of Mumford curves
An origami (also known as square-tiled surface) is a Riemann surface covering a torus with at most one branch point. Lifting two generators of the...
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The Isomorphism Problem for All Hyperbolic Groups
We give a solution to Dehn’s isomorphism problem for the class of all hyperbolic groups, possibly with torsion. We also prove a relative version for...
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Isometry types of profinite groups
Let T be a rooted tree and Iso( T ) be the group of its isometries. We study closed subgroups G of Iso( T ) with respect to the number of conjugacy...