Upper join of characteristic subgroups

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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]

Definition

A subgroup H of a group G is termed an upper join of characteristic subgroups if there exist subgroups K_i,i \in I of G containing H (where I is an indexing set) such that:

Note that H need not be a characteristic subgroup of G because characteristicity is not upper join-closed.

Formalisms

In terms of the upper join-closure operator

This property is obtained by applying the upper join-closure operator to the property: characteristic subgroup
View other properties obtained by applying the upper join-closure operator

Relation with other properties

Stronger properties

Weaker properties