Large Sets in Boolean and Non-Boolean Groups and Topology

TL;DR

This paper explores the properties of various large sets in Boolean and non-Boolean groups, examining their topological aspects and relationships with ultrafilters to deepen understanding of group structure and set interactions.

Contribution

It introduces new insights into the interplay of large sets in Boolean groups and their associated topologies, linking fat sets with ultrafilters.

Findings

Characterization of fat sets and their topological properties

Relations between fat sets and ultrafilters in Boolean groups

Insights into the structure of large sets in group theory

Abstract

Right and left thick, syndetic, piecewise syndetic, and fat sets in groups are studied. The main concern is the interplay between such sets in Boolean groups. Natural topologies closely related to fat sets are also considered, which leads to interesting relations between fat sets and ultrafilters.