# Pathological abelian groups: a friendly example

## TL;DR

This paper presents a simple example of an abelian group with multiple complex and pathological properties, highlighting its significance in understanding such groups.

## Contribution

It introduces the group of bounded sequences over 1f6z[1f6z] as a new, simpler example of a pathological abelian group.

## Key findings

- The group exhibits several well-known pathological properties.
- It is simpler than previously known examples for some properties.
- It is easier to describe than earlier examples.

## Abstract

We show that the group of bounded sequences of elements of $\mathbb{Z}[\sqrt 2]$ is an example of an abelian group with several well known, and not so well known, pathological properties. It appears to be simpler than all previously known examples for some of these properties, and at least simpler to describe for others.