ﻻ يوجد ملخص باللغة العربية
We show that word hyperbolicity of automorphism groups of graph products $G_Gamma$ and of Coxeter groups $W_Gamma$ depends strongly on the shape of the defining graph $Gamma$. We also characterized those $Aut(G_Gamma)$ and $Aut(W_Gamma)$ in terms of $Gamma$ that are virtually free.
We provide new examples of acylindrically hyperbolic groups arising from actions on simplicial trees. In particular, we consider amalgamated products and HNN-extensions, 1-relator groups, automorphism groups of polynomial algebras, 3-manifold groups
The superextension $lambda(X)$ of a set $X$ consists of all maximal linked families on $X$. Any associative binary operation $*: Xtimes X to X$ can be extended to an associative binary operation $*: lambda(X)timeslambda(X)tolambda(X)$. In the paper w
A detailed proof is given of a theorem describing the centraliser of a transitive permutation group, with applications to automorphism groups of objects in various categories of maps, hypermaps, dessins, polytopes and covering spaces, where the autom
We show that the automorphism group of a graph product of finite groups $Aut(G_Gamma)$ has Kazhdans property (T) if and only if $Gamma$ is a complete graph.