# 3k-4 theorem for ordered groups

## TL;DR

This paper provides elementary proofs for two recent structure theorems concerning ordered groups, simplifying the understanding of their algebraic properties.

## Contribution

It offers accessible, elementary proofs of complex theorems in the theory of ordered groups, making these results more widely understandable.

## Key findings

- Elementary proofs of two structure theorems for ordered groups
- Simplification of existing complex proofs
- Enhanced understanding of ordered group properties

## Abstract

Recently, G. A. Freiman, M. Herzog, P. Longobardi, M. Maj proved two `structure theorems' for ordered groups \cite{FHLM}. We give elementary proof of these two theorems.