The Structure of Divisible Abelian Groups

TL;DR

This paper provides a detailed exposition of the structure theorem for divisible abelian groups, showing they decompose into sums of rationals and quasicyclic groups.

Contribution

It offers an in-depth, detailed proof of the structure theorem for divisible abelian groups, enhancing understanding of their composition.

Findings

Divisible abelian groups decompose into sums of additive rationals and quasicyclic groups.

The paper clarifies the proof of the structure theorem for these groups.

Provides a comprehensive exposition for educational purposes.

Abstract

This is an expository work presenting in detail the proof of the structure theorem for divisible abelian groups. A divisible abelian group is an abelian group that satisfies nD=D for all natural n. The theorem states that any divisible group is a direct sum of copies of the additive rationals and quasicyclic groups.