[Publications][Nicolas Monod]

Kaleidoscopic groups: permutation groups constructed from dendrite homeomorphisms

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 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.

Authors: B. Duchesne, N. Monod, P. Wesolek

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[Publications][Nicolas Monod]