Strongly characteristic 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

Stronger properties

 * Weaker than::Strongly fully characteristic series

Weaker properties

 * Stronger than::Characteristic series
 * Stronger than::Normal series
 * Stronger than::Subnormal series