# Characteristic series

From Groupprops

This article defines a property that can be evaluated for a subgroup seriesView a complete list of properties of subgroup series

## Contents

## Definition

A subgroup series of a group is termed a **characteristic series** if all members of the series are characteristic subgroups of the whole group.

## Relation with other properties

### Stronger properties

- Strictly characteristic series
- Fully characteristic series
- Strongly characteristic series
- Quotient-strongly characteristic series