Return to Glossary.

Formal Definition

A group is simple if it is nontrivial and has no proper nontrivial normal subgroups.

Informal Definition

Replace this text with an informal definition.


The alternating group $A_{n}$ is simple for $n\geq5$.


$S_{n}$ is not a simple group for $n\geq3$ because $A_{n}$ is a normal subgroup.

Additional Comments

Add any other comments you have about the term here

Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License