Characteristically complemented normal subgroup
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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]
A subgroup of a group is termed a characteristically complemented normal subgroup or characteristically complemented direct factor if it is a direct factor in an internal direct product where the other direct factor is a characteristic subgroup.
Relation with other properties
- Characteristically complemented characteristic subgroup: For proof of the implication, refer Characteristically complemented characteristic implies characteristically complemented normal and for proof of its strictness (i.e. the reverse implication being false) refer Characteristically complemented normal not implies characteristically complemented characteristic.
This subgroup property is transitive: a subgroup with this property in a subgroup with this property, also has this property in the whole group.
ABOUT THIS PROPERTY: View variations of this property that are transitive | View variations of this property that are not transitive
ABOUT TRANSITIVITY: View a complete list of transitive subgroup properties|View a complete list of facts related to transitivity of subgroup properties |Read a survey article on proving transitivity
This subgroup property is quotient-transitive: the corresponding quotient property is transitive.
View a complete list of quotient-transitive subgroup properties