Compactness in abelian group theory

TL;DR

This paper explores the extension of classical compactness theorems in abelian group theory, focusing on large cardinals and the structure of direct sums of cyclic groups.

Contribution

It generalizes two classical compactness results from free abelian groups to direct sums of cyclic groups, broadening the theoretical framework.

Findings

Generalized compactness theorems to broader classes of abelian groups

Connected large cardinals with properties of abelian group structures

Enhanced understanding of the structure of direct sums of cyclic groups

Abstract

In this paper we discuss large cardinals and compactness theorems in abelian group theory. More specifically, we generalize two classical compactness results for free abelian groups to the broader context of direct sums of cyclic groups.