Kaleidoscopic groups: permutation groups constructed from dendrite homeomorphisms
Abstract
Given a transitive permutation group, a fundamental object for studying its higher transitivity properties is the permutation action of its isotropy subgroup. We reverse this relationship and introduce a universal construction of infinite permutation groups that takes as input a given system of imprimitivity for its isotropy subgroup. This produces vast families of kaleidoscopic groups. We investigate their algebraic properties, such as simplicity and oligomorphy; their ho-mological properties, such as acyclicity or contrariwise large Schur mul-tipliers; their topological properties, such as unique polishability. Our construction is carried out within the framework of homeomor-phism groups of topological dendrites.
Domains
Group Theory [math.GR]
Origin : Files produced by the author(s)
Loading...