# Not all groups are LEF groups, or can you know if a group is infinite?

## TL;DR

This paper introduces the class of locally embeddable into finite groups (LEF groups), exploring their properties and significance in group theory.

## Contribution

It provides an introduction and foundational overview of LEF groups, clarifying their characteristics and importance.

## Key findings

- LEF groups are a significant class in group theory
- Not all groups are LEF groups, especially infinite groups
- Understanding LEF groups aids in the study of group approximations

## Abstract

This is an introduction to the class of groups that are locally embeddable into finite groups.