# Group of finite chief length

From Groupprops

This page describes a group property obtained as a conjunction (AND) of two (or more) more fundamental group properties: group satisfying ascending chain condition on normal subgroups and group satisfying descending chain condition on normal subgroups

View other group property conjunctions OR view all group properties

*This property makes sense for infinite groups. For finite groups, it is always true*

This is a variation of finiteness (groups)|Find other variations of finiteness (groups) |

## Contents

## Definition

A **group of finite chief length** is a group satisfying the following equivalent conditions:

- It possesses a chief series of finite length, i.e., a normal series of finite length that cannot be further refined.
- It satisfies the ascending chain condition on normal subgroups as well as the descending chain condition on normal subgroups.