Characteristically DP-decomposable 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]

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]


Definition with symbols

A subgroup H inside a group G is said to be characteristically DP-decomposable if we can express G as an internal direct product of subgroups G_w such that H is the internal direct product of all the H_w = H \cap G_w, and further, each H_w is characteristic in G_w.

Relation with other properties

Stronger properties

Weaker properties


Direct product-closedness

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.