Characteristically DP-decomposable subgroup
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]
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Definition with symbols
A subgroup inside a group is said to be characteristically DP-decomposable if we can express as an internal direct product of subgroups such that is the internal direct product of all the , and further, each is characteristic in .
Relation with other properties
This subgroup property is direct product-closed: it is closed under taking arbitrary direct products of groups
This actually follows from the way it's defined. The given property is the strongest direct product-closed subgroup property that is weaker than the property of being characteristic.
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).
View other trim subgroup properties | View other trivially true subgroup properties | View other identity-true subgroup properties
Clearly, the trivial subgroup, as well as the whole group, are characteristically DP-decomposable.