Arithmetic Sets in Groups

TL;DR

This paper introduces the concept of arithmetic sets within arbitrary countable groups and explores their properties specifically in Abelian and non-Abelian free groups.

Contribution

It defines arithmetic sets in general groups and investigates their characteristics in both Abelian and free non-Abelian groups.

Findings

Properties of arithmetic sets in Abelian groups

Characteristics of arithmetic sets in free groups

Differences between Abelian and non-Abelian cases

Abstract

We define a notion of an arithmetic set in an arbitrary countable group and study properties of these sets in the cases of Abelian groups and non-abelian free groups.