Strongly characteristic series

This article defines a property that can be evaluated for a subgroup series

View a complete list of properties of subgroup series

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:

• Frattini series
• Derived series

Relation with other properties

Stronger properties

• Strongly fully characteristic series

Weaker properties

• Characteristic series
• Normal series
• Subnormal series