Serial subgroup

In terms of the serial closure operator
The property of being a serial subgroup is obtained by applying the serial closure operator to the subgroup property of being normal.

Stronger properties

 * Weaker than::Ascendant subgroup
 * Weaker than::Descendant subgroup
 * Weaker than::Subnormal subgroup
 * Weaker than::2-subnormal subgroup
 * Weaker than::Composition subgroup

Related group properties

 * Absolutely simple group is a group that has no proper nontrivial serial subgroup. Thus, this property is obtained by applying the simple group operator to the subgroup property of being simple

Metaproperties
Since any serially closed subgroup property is transitive, the property of being a serial subgroup is a transitive subgroup property.

The property of being a serial subgroup is trim, because the property of being normal is itself trim.