Kaleidoscopic groups: permutation groups constructed from dendrite homeomorphisms
Group Theory
2021-04-29 v1
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 kaleidoscopic groups. We investigate their algebraic properties, such as simplicity and oligomorphy; their homological properties, such as acyclicity or contrariwise large Schur multipliers; their topological properties, such as unique polishability. Our construction is carried out within the framework of homeomorphism groups of topological dendrites.
Cite
@article{arxiv.1801.09787,
title = {Kaleidoscopic groups: permutation groups constructed from dendrite homeomorphisms},
author = {Bruno Duchesne and Nicolas Monod and Phillip Wesolek},
journal= {arXiv preprint arXiv:1801.09787},
year = {2021}
}