An action of a group on a set is called k-transitive if it is transitive on ordered k-tuples and highly transitive if it is k-transitive for every k. We show that for n ≥ 4 the group Out(Fn) = Aut(Fn)/ Inn(Fn) admits a faithful highly transitive action on a countable set.

Abstract Associated with each finite subgroup $\Gamma $ of ${\textrm{SL}}_2({\mathbb{C}})$ there is a family noncommutative algebras $O_\tau (\Gamma )$ quantizing ${\mathbb{C}}^2/\!\!/\Gamma $. Let $G_\Gamma be the group $-equivariant automorphisms In [ 16], one authors defined and studied natural action on certain quiver varieties associated He established bijective correspondence between spac...

Objectives: Nouns and verbs are the central conceptual linguistic units of language acquisition in all human languages. While the noun-bias hypothesis claims that nouns have a privilege in children’s lexical development across languages, studies on Mandarin and Korean and other languages have challenged this view. More recent cross-linguistic naming studies on children in German, Turkish,...

The regular polyhedra have the highest order of 3D symmetries and are exceptionally attractive templates for (self)-assembly using minimal types of building blocks, from nano-cages and virus capsids to large scale constructions like glass domes. However, they only represent a small number of possible spherical layouts which can serve as templates for symmetric assembly. In this paper, we formal...

A subgroup G of automorphisms of a graph X is said to be 2 -arc-transitive if it is vertexand edgebut not arc-transitive. The graph X is said to be 2 -arc-transitive if Aut X is 1 2 -arc-transitive. The interplay of two different concepts, maps and hypermaps on one side and 2 -arc-transitive group actions on graphs on the other, is investigated. The correspondence between regular maps and 2 -ar...