Characteristically complemented characteristic subgroup
This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: characteristically complemented subgroup and characteristic subgroup
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Relation with other properties
- Left-transitively complemented normal subgroup
- Characteristic direct factor
- Characteristically complemented subgroup
- Complemented characteristic subgroup
- Complemented normal subgroup
- Normal subgroup
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
Suppose are groups such that is a characteristically complemented characteristic subgroup of and is a characteristically complemented characteristic subgroup of . Then is a characteristically complemented characteristic subgroup of . For full proof, refer: Characteristically complemented characteristic is transitive
This subgroup property is trim -- it is both trivially true (true for the trivial subgroup) and identity-true (true for a group as a subgroup of itself).
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