Universal groups of intermediate growth and their invariant random subgroups

TL;DR

This paper constructs examples of universal groups with intermediate growth that possess a vast number of invariant random subgroups, expanding understanding of group growth and subgroup structures.

Contribution

It introduces universal groups of intermediate growth with a continuum of invariant random subgroups, a novel combination in group theory.

Findings

Existence of universal groups with intermediate growth and many invariant random subgroups.

These groups have $2^{ ext{aleph}_0}$ ergodic, continuous, invariant random subgroups.

The examples are associated with a family of groups of intermediate growth.

Abstract

We exhibit examples of groups of intermediate growth with $2^{\aleph_0}$ ergodic, continuous, invariant random subgroups. The examples are the universal groups associated with a family of groups of intermediate growth.