On Limit Aperiodic G-Sets

TL;DR

This paper investigates the property of limit aperiodicity in G-sets, demonstrating its preservation under common group constructions and providing an example of a non-limit aperiodic G-space.

Contribution

It establishes that limit aperiodicity is preserved under extensions, HNN extensions, and free products, and constructs a G-space that is not limit aperiodic.

Findings

Limit aperiodicity preserved under group extensions, HNN extensions, free products.

Constructed a non-limit aperiodic G-space.

Provides theoretical insights into the structure of G-sets.

Abstract

We prove that the property to be limit aperiodic is preserved by the standard construction with groups like extension, HNN extension and free product. We also construct a non-limit aperiodic G-space.