# Group of composition length two

From Groupprops

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism

View a complete list of group propertiesVIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

## Contents

## Definition

A **group of composition length two** is a group whose composition length is *at most* two. In other words, it satisfies one of these three cases:

- It is a trivial group.
- It is a simple group.
- It has a simple normal subgroup such that the quotient is also simple; in other words, it has a simple maximal normal subgroup.