# Strongly 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 **strongly characteristic series** if every smaller member of the subgroup series is a characteristic subgroup in every bigger member.

## Examples

Any subgroup series obtained by iterating a subgroup-defining function is a strongly characteristic series. Here are two examples: