On sum-free subsets of abelian groups

TL;DR

This paper explores the properties and characteristics of sum-free subsets within abelian groups, addressing their quantity, maximum size, typical structure, and specific examples.

Contribution

It provides a comprehensive, accessible analysis of sum-free subsets in abelian groups, including counts, maximum sizes, and structural insights.

Findings

Quantifies the number of sum-free subsets in abelian groups

Identifies maximum cardinality of sum-free subsets

Describes typical structure of sum-free subsets

Abstract

In this paper we discuss some of the key properties of sum-free subsets of abelian groups. Our discussion has been designed with a broader readership in mind, and is hence not overly technical. We consider answers to questions like: how many sum-free subsets are there in a given abelian group $G$? what are its sum-free subsets of maximum cardinality? what is the maximum cardinality of these sum-free subsets? what does a typical sum-free subset of $G$ looks like? among others.